I love the British version, myself, because it's a very contained, well-written story arc. David and Tim both have a strong start, middle, and end to their stories, and that really appeals to me. The US version I could never get into since it feels far less real. It's just another sitcom where the characters get up to vaguely wacky hijinks every week.
I like US
The Office, but UK
The Office was a really great show that lasted exactly as long as it should have, and had a perfect ending. But it's not a classic sitcom - there are other British shows that are, but this one wasn't, it was as much drama as it was comedy, and the documentary feel was a big part of the appeal. It really was quite depressing, though - and the funniest parts were also those that made you feel really embarrassed for the characters (David Brent, mostly).
As for the characters, I think the US version did a good job with Michael Scott, he's a good character in his own right even though it was a tough job following up on Ricky Gervais' David Brent. But the biggest difference in the two versions, for me, is that Tim was a much more sympathetic character than Jim, and I cared about him and Dawn a great deal more than I ever did about Jim and Pam; while Dwight is very different from Gareth, a lot more likable but also less convincing and more of a caricature. Gareth was a complete jerk, but he was a very realistic character. Dwight is way too out there. On the other hand, the US version makes up for the (IMO) less compelling central characters with developing many of the supporting characters a lot more than the UK version did (maybe because it lasted shorter).
I'm sure someone else said this already, but I suppose it just depends on your ability to enjoy British humor. The UK version of The Office is about as strong a brand of British comedy as you're going to get. If British comedy is not your thing, or if it tends to be hit/miss with you, then there's a good chance you're not going to dig The Office.
Nothing wrong with that. It sure as hell isn't for everyone.
That's a very broad statement. How many popular UK comedy series have you watched? Have you "Only Fools and Horses"? That's a completely different brand of humor than "The Office", and a lot more like a classic character comedy combined with drama. And there are lots of shows which are very much like classic sitcoms, like "Coupling". What about "Allo Allo"? A laugh-out-loud farce, not subtle at all. Then there's the satire of "Blackadder". Then the surrealist humor of "Monty Python's Flying Circus". There is no such thing as "British humor", since there are lots of different types of British humor.