I like Kobe very much. It feels like a very 'international' place downtown, but it's not overly large. Once you leave downtown, things can get very local. It's also also just a hop away from Osaka and two from Kyoto, which makes it a day trip away from a good chunk of Japanese culture.
I'm afraid I can't compare it much with other cities, as I've spent much more time in Kobe than anywhere else, and it's only been a few months so far.
I'll just butt in to say Kobe is great. Lots of character and interesting places to hang out in. Has it's own charm, different from Osaka or Nagoya (which I really like too).