Old Ones, Gods, Devils and Angels

It is a common conceit among those who are fans of the Cthulhu mythos that Lovecraft's entities are greater in power than the more traditional, humanistic sort of deities found in pantheons within real history, or of eldritch horrors found in other fiction.  There is also this sort of belief that the Lovecraftian entities are something worse than "evil" since they are an entirely alien sort of entity that doesn't even understand or care about humanity at all.  In stories that contain both Lovecraftian entities and beings from more standard myths, the Lovecraftian styled entities are largely implied to be more powerful and very difficult to contend with.  The truth is that the Lovecraftian entities aren't really all that different from the entities of other myths or fiction.  Now this is not going to be a perfect comparison since power at the scale cannot really be objectively measured.  Everything involved is highly conceptual in nature and pretty much ignores such things as physics.


That is not Dead which can eternal lie, and with strange aeons even death may die.

One of the things that people point to for the overwhelming power of Lovecraft's entities over those of other sources is the explicit fact that beings like Cthulhu can't really die in the commonly accepted meaning of the word.  Cthulhu is mentioned to be in a death-like sleep but that this status is temporary.  Cthulhu, like several other Old Ones and Great Old Ones and so on are basically implied as being unable to actually die.  As such there is always a chance that they might come back.  This is compared to other pantheons wherein supposedly the Gods can die.  However, this needs to be looked at as well.

In Greek myth, the Gods and Titans do not actually die.  Chronos, after being cut up into multiple pieces is then locked in Tartarus due to the fact that no matter how much damage is done to him, he cannot really die.  The same is implied to be true of all the Gods in the Greek pantheon.  They can be harmed and injured and devoured (as Zeus did to Metis), but they can't really die.  This is similarly the case for most pantheons.  In fact, in most real world myths, nothing really ever dies.  Even for humans death is simply a change from one state to another.  The idea of Cthulhu or anything else being essentially unkillable is rather a normal facet of a myth instead of being an indicator of how powerful Lovecraftian entities are.  The one major exception would seem to be the Aesir and other Nordic myths, for whom death, the rare times it happens, is actually permanent.  Even there, however, death is just a transition to Helheim or Valhalla.  The entity still exists.  In fact, in some versions of the Ragnarok myth, Baldur comes back to life after Ragnarok is over.

Likewise, this goes for the same in some fictional settings. 

The beings within Tolkien's legendarium are also essentially immortal at their most basic level.  The Ainur, the divine spirits that came to Arda to guide its life cycle, are primarily non-physical entities.  With the blessing of Eru they can take physical form in order to interact with the world that Eru had created.  In a normal case, the Ainur can take up a physical form or drop it relatively easily.  If their physical form is some how destroyed, it takes them longer to create a new one.  Also, if the particular spirit has been serving their own interests rather than those of Eru, it is possible and even likely that they will not be able to recreate a physical form.  As such, Fallen Ainur such as Morgoth, Sauron and the Balrogs become more and more tied to their physical form and less able to change it or create a new one.  Morgoth got around this by creating the Iron Crown, which would serve as an anchor for his spirit to return to Middle Earth.  So long as the crown existed in Middle Earth, he would be able to return.  The Iron Crown is the basic concept used by Sauron in the creation of the One Ring.  In both cases, they allowed the spirit to create a new body after losing the old ones.  Even when the Ring is destroyed, Sauron is not killed, he is merely made impotent.  From that point on, he is only a shadow capable of creating fear and doubt in the area near him, but even that only weakly.  If Eru were an uncaring creator deity such as Azazoth, then Sauron and Morgoth would be exactly as unkillable as any of the old ones because they would always be able to come back to it eventually.

Corruption of Realms and People

A lot of is made of the fact that the Outer Gods and the Great Old Ones can tinker with the nature of people and use that create things like the people of Innsmouth or bizarre, otherworldly realms wherein the normal laws of physics seem to have no sway.  However, the impact on the physical world as evidenced by Cthulhu is rather mild compared to other pieces of fiction.  Compare to the Greek Gods, which can alter the climates on a whim and frequently do or the Tolkien legendarium where the climate and terrain around a major power like Morgoth or even someone as low as Elrond, begins to grow and develop to match the character and nature of its master.  As to the corruption of people, look to orcs, trolls, nazghul, gollum and Black Numenoreans for examples of how Tolkien's spiritual agents can alter the people around them.  For real world myth you have all manners of stories where in the gods curse sometimes entire groups.  Even the relatively low power type gods in the Forgotten Realms setting are able to magically alter humans and others.  For the effect of angels and demons on humanity in the Abrahamic religions, look up the stories of nephilium and witches, also note the stories of 40 days and nights of rain, or the way that YHWH or whoever will occasionally blast an area with crippling drought.

Insanity on Sight or Exposure

Once again, this is not an unusual facet of mythological beings.  Looking at angels will turn you to salt, if you're lucky.  Looking at the true form of a Greek god will burn you to a pile of ashes in a moment, as shown when Hera tricked one of Zeus's lovers to demand that he prove himself by showing his true appearance.  Sauron, on his own at the lowest apex of his dwindling power, was able to drive people insane merely by observing them from a distance.  The only difference between Cthulhu and most mythological beings in this case is their willingness to expose their true natures.  The Great Old Ones don't care about people, so they rarely if ever have a reason to conceal their sanity-warping forms.  Meanwhile the gods of most pantheons regularly go around in some easily understandable form rather than constantly sending their followers into fatal seizures or worse.

Azazoth - Creator and Destroyer

 Of course, not Lovecraft fan is going to get in this discussion without bringing the single most powerful entity of the mythos and pointing out that Azazoth will eventually destroy the universe and that nothing can stop it.  Only by keeping it asleep using the multitude of demonic musicians circling it, is Azazoth kept at bay.  However, Azazoth is really no different in that regards from other creator entities.  Eru and YHWH, considered essentially the same entity really, both created the universes in which they dwelled as well.  Now someone is going to say "but Eru and YHWH each created a single planet, not a whole universe."  This is a flawed perspective.  While the stated myths of such things only indicate Earth, that's largely because that's the part of reality focused on in the stories.  It is explicitly stated in both cases that the entity created the entire universe of the setting.  In Eru's case, he even simply altered the entire nature of that setting in order to make people unable to reach Valinor without help.  At first the world was flat and connected straight to Valinor.  After the sinking of Numenor, sailing west only resulted in finding new realms (which did not get mentioned in the novel).  It is likely that he eventually altered the shape of the heavens in order to prevent humans from reaching the spiritual planes by going up and instead only allowed them to find more physical places to go to.

Limits

Now this is something.  Lovecraft's entities have limits, hard limits that they can't work around and are not taken on just by their own decision.  Most pantheon entities likewise have similar limits.  Quite often their is a trace of "gods need prayer" going on wherein the prayers of the mortals keep the gods alive and empowered so that they might be able to effectively counter whatever monstrosities.  Monotheistic beliefs such as the Abrahamic religions, Tolkien's legendarium (again, very much based on his belief in the Catholic faith), several Native American religions and reportedly most African religions (though I have not studied this much) all have all-powerful monotheistic entities that don't need anything from us and can't be affected by us much at all.  Such monotheistic entities don't need help from humans to come back into the world (Cthulhu) and they aren't put to sleep like the blind, idiot demon-sultan (Azazoth).  They are literally All-Powerful and capable of doing whatever they wish to do as adverse Lovecraft's creatures which bound, sealed, and so on.  That said.  The Lovecraft entities compare fairly equivalently in limits to the gods and other entities of pantheistic mythologies.

Conclusion

It is up to the individual author how strong any god is in comparison with other gods, however, there is nothing in the Cthulhu mythos that necessitates Lovecraft's being supreme over things like the Greek gods, Sauron or so on.  The Lovecraftian entities have conceptually the same sort of powers and characteristics common to mythological entities for thousands of years.  There is nothing exceptional about their power level as compared to that of other gods, demons and angels and indeed even Azazoth falls short of the power levels shown in monotheistic religions. 

There is only one thing that sets Lovecraftian style entities apart from other pantheons: the relationship with people.

In most pantheons, humanity was created specifically by a creator entity and several laws of behavior were handed down.  Thus, while the gods or God are, indeed, supremely powerful, alien entities, they have an image that is easier to relate to than that of the majority of the Lovecraftian entities.  In Lovecraft's storyline, humanity is an accidental byproduct of the experiments by the Elder Things.  They didn't pop up right away, evolving out of the various forms of life that came to be when the Elder Things' experiments went crazy.  As such, the entities of that setting have had little to no contact with humans and have almost no relation in terms of morality or imagination with humanity as a whole.

So, while the Cthulhu mythos entities aren't any more powerful than the Greek Gods or Titans, the Lovecraftian entities don't see humans as fun little playtoys, but rather tend not to think about them at all, or perhaps think of them just as a sort of vermin.  Their deprecations against humanity as a result are largely incidental to their other actions rather than deliberate acts of evil.  Unfortunately, it also means that they don't see a need to rein in their power the way the gods of other settings would in order not to break their cool stuff.

Again, Zeus and company see humans as fun and interesting and thus have an interest in not breaking them.  Cthulhu and company barely think about humanity and thus have no similar interest in not breaking them.  That's the major difference.  Power and abilities beyond that are pretty much on level with other world settings.