oneallanclarke They're quite different. The Danish guy is a right dry miserable bastard, but the shows are really good and the dry sense of humour appeals to me. The UK version is also good, and totally different in pacing and humour. Both are worth a watch.
As you say UK remakes often lose the charm and wit of the originals in their quest to be zany or controversial - Professor T is a classic example of that - they Belgian original was fab, but the UK version I found unwatchable. Same goes for the French Astrid and Raphaelle (based around an autistic researcher) which had a UK version recently which was awful.