(side note: death metal, like black metal, has a really bad tradition of naming styles after the area they first sprung up in, even after they've spread globally. Hence why you'll sometimes hear things like a japanese band being termed 'New York' death metal.)
Melodeath is originally a european (actually a Gothenburg, Sweden) innovation, so it's not too surprising to see them at the forefront of that style. Especially when the most influence melodeath has had in the US is metalcore bands imitating At The Gates leads and guitar harmonies. Not sure that I'd call Dimmu Borgir death metal, but I haven't listened to any of their work since Stormblast, so I'll defer to you on that.
Originally, euro DM was the sloppy one. DM began branching into different styles almost as soon as it was created, early on there was the florida sound (essentially downtuned, harsher thrash eventually changing into what's now considered death metal) and the swedish sound (not to be confused with melodeath, it was a rougher and rawer style owing more to hardcore bands like Discharge than it did to thrash). The swedish style kind of died in the melodeath surge though.
Of the styles that have sprung up since then, the sloppiest (slam-death, or texas DM, which probably isn't what you've heard) is pretty much an American phenomenon while the cleanest (technical death metal) is a mostly european style. Excluding melodeath, euro DM does tend to be a bit cleaner but it's largely a matter of which style the band actually plays.
This is getting a bit long, so I'll namedrop a few tighter DM bands in the next post.