The two are not contradictory, but more of a contextual plot point for their individual movies.
Let's first ignore the specifics of "What is the power of Thor". We may assume it comes with increased strength/durability, power over lightning etc., but the details don't really matter in this context.
In this movie, Thor does something un-worthy. Odin is banishing Thor to Midgard, after first stripping away his powers. This is meant as a lesson, and the hammer is sort of a conduit for that lesson. Odin literally removes Thor's armour, his powers, and then casts him out.
He then whispers into the hammer
Whosoever holds this hammer, if he be worthy, shall possess the power
The inscription appears on the hammer at this time.
In the context of this movie, Thor initially had the power of Thor. The power of Thor was removed from him. Thor on Earth doesn't have some of the basic benefits we tend to see with Thor in general, he's more easily restrained by normal humans, more susceptible to normal injury, etc.
A spell was cast on the hammer, to make it so that the person who wields the hammer, if they are worthy, will gain the power of Thor. In the context of the person Thor, this is more accurately re-gaining the amount of power that was stripped from him earlier. Given the preachy nature of Odin in general, it seems somewhat clear that the only person expected to pick up Mjolnir is Thor himself.
It's more of a one-time transaction where the hammer fuels the enchantment, but is more of a temporary storage of power rather than a constant source of power. Once the power is given back to Thor, by virtue of worthiness, the wielder of the power of Thor is the person Thor, not the hammer Mjolnir. The effect of that enchantment ends here.
Thor loses his hammer. He had a special and intimate relationship with that hammer. He feels powerless without it. He needs to learn that he is the God of Thunder, not the God of Hammers. His power isn't limited to what he can pull off with the hammer.
This is an independent lesson, not particularly connected to the lesson in Thor (2011). Although one could argue that the lesson in Thor (2011) could easily have given both Thor, and the viewer, the impression that the hammer was the source of the power.
I'll come back to this answer with video clips etc. as supporting evidence - am at work now on a break so not an option.