PWS: I don't think we can really judge what is going to happen with the US show based on the British show. Because the British show was only 2 seasons long, and each season was only 6 or so episodes. So, in terms of number of episodes, I believe the US version has surpassed the British version.
Anyhow, for what it is worth:
Tim stayed with the company for the duration of the show (aka Jim. In fact, there was no talk of Tim leaving to join the other branch). After the 2 seasons, they made a final episode called The Office Special; it was set 3 years after the documentary finished filming (sort of like those reality tv show reunions they have with former castmates). Dawn had moved to Florida with her fiancee (his sister was living there) and was babysitting for a living. The last part of the episode is the company having a Christmas party and Dawn comes back (the documentary crew interviewed her in Florida & she spoke about how she couldn't afford to come home for Christmas so the documentary crew ended up paying for her flight). Anyway, she comes to the party and she and Tim start kissing and become a couple and that's how the show ends.
In the British version, the two branches of the company do merge (like in the American show, there was always talk about branches closing or merging. Whether that will happen in the US show remains to be seen). The boss character gets demoted (the other branch manager becomes the boss). In the special you see how the boss has been fired (or quit, can't remember which) and is now making a living as a former reality tv star, making stupid appearances and stuff. And Gareth (aka Dwight) is now the manager.
It would have been great if Rainn Wilson had gotten nominated for an Emmy. Ah, well. They got nominated for 5 awards in all - show, actor, writing and I forget what the other 2 were.