I've had some experience with Pygame, but there seems to be a lot of buzz around Pyglet these days.
How do these two libraries compare? What would be the advantage of using one over the other, both in features and ease of use?
Finally, would you say that one is more Pythonic than the other?
Pyglet is good (for 2D games) if you never intend to draw any vector graphics or primitives within the game itself, and just stick to loading images from disk. It's also much cleaner because there's no need to write your own game loop and have to worry about speed and timing and responsiveness.
However, if you ever have to generate graphics on-the-fly, and then save them, either as a variable or as a file, then pyglet becomes considerably more complicated because you start having to muck around with the low-level OpenGL functions. In those scenarios, pygame is much more user-friendly, with its software rendering and Surface class. Or you could use Python Imaging Library and interface it with pyglet.
Obviously, for 3D games, you are going to have to muck around with OpenGL functions anyway, in which case I recommend pyglet over pygame + PyOpenGL.
Differences between Python game libraries Pygame and Pyglet?