This topic has been discussed many many times here from many different angles. I would encourage you to use our search engine; type in European or European vs American and you will find more than you can likely read. There are differences between the two types, but what will suit you best depends on what you are looking for in your doberman.
Just to get you started, this link is a discussion of many of the differences between the two, written by Kansadobe, a breeder here on DT whose bloodlines include both American and European dogs: American vs. Euro
For me personally, one of the biggest factors between choosing Euro vs American dobes, when you don't have any need for a particular specialized trait (where one might do better than the other) is the ease of finding a reputable breeder. It is so important that you find a breeder who can serve as your resource for the life of your dog, and here in the US, it's much easier to find a good breeder who breeds American bloodlines. There are definitely good Euro breeders out there, but not as many.
The term "European bred" can be a marketing gimmick; there are bad breeder/greeders out there who are using the Euro tag line as a selling point to mislead people into thinking that their dogs are something special that are worth paying extra for. Unsuspecting folks think bigger is better, and that a Euro bred dog is automatically more massive and has fewer health problems with a US dog. But often the folks who are selling their dogs with that tagline aren't using particularly good breeding stock and are counting on roping in the unsuspecting buyer for their "more authentic doberman" Often they even charge more because their bloodlnes are "special" (their words)