Well I guess if I had to make a generalization I prefer manga over mainstream Western comics (I don't know enough about indie comics to give an opinion on them). The differences that particularly stand out to me are:
Self-contained stories that end: This is a personal preference more than anything, but I find the mess of continuity and tie-ins in a lot of the American comics I've read confusing. I think that one writer producing a story with a definite beginning, middle and end allows for a lot more variety, creativity and expression as far as storytelling goes.
Black and white art: This is entirely a personal preference, but I have a thing for negative space. I also mostly do black and white work when I draw, so I have a better appreciation of the techniques involved than I do with color work.
Panel layout and transitions: I generally find that the Japanese comics I read have a better and more dynamic flow from panel to panel and from page to page as well as using a much wider variety of transitions between scenes (mostly adapted from cinema).
To give an idea of the experience I'm basing this on, my favorite Western comics are Hellboy, Watchmen, The Long Halloween and Tin Tin and I've had a fair amount of exposure to all the major superhero books and the stuff Vertigo publishes. I read a lot more Japanese stuff (I can read Japanese and I'm currently living in Japan, so that's only natural), but my favorites include Devilman, Monster, Vagabond, Akumetsu and Swan.
Mainstream Japanese comics definitely have far more variety than their American equivalents as a result of serving a far more diverse audience (my list of favorites included a cold war commentary about an army of demons from the south pole, a mystery/thriller about a surgeon in Germany chasing after a serial killer, a historical drama based on the life of Miyamoto Musashi and a series about ballet).
DO NOT BUY the Ghost in the Shell sequels. They are all terrible. Honestly, a Masamune Shirow series is probably a terrible place to start reading manga. Avoid all the Shonen Jump stuff too, as it's intended for 8-14 year olds and goes on forever. If you tell me what you like in Western comics I can probably give you some recommendations.