Well, I'm not an IPA whiz, but as I understand it, I think the I sound in both dialects is closer to your second example. And the second, unstressed vowel is also pronounced in both, though perhaps a bit more distinctly in the US one. Generally speaking, I'd say that the pronunciation is a lot more similar for this word than it is for many.

Both pronunciations would be understandable. There is a very popular (and very long running) show in America called "The Simpsons" In the Title song it's pronounced [ˈsɪmpsənz], but through out the show it is normal to hear the name pronounced either way. I think the primary difference between the two pronunciations in America is how fast the person saying it is speaking (and possibly whether or not they're from the South, people from the South tend to be more willing to schwa vowel sounds.)