This depends entirely on where you want to go. A British accent is more novel and unusual in the U.S. than an American accent is in Britain - but not by much. The only thing you want to avoid is too much of an accent - a British accent from Liverpool, for example, or an American accent from deep Lousiana. The point is to be understood, wherever you go.

You might also consider that words and sometimes even sentence structure may be different in British English than in American English. For example, in British English the trunk of a car is called a boot. If you begin learning British English you may want to keep using British English because you are more familiar. As far as sentence structure, here is an example: British English: Three people were injured and taken to hospital. American English: Three people were injured and taken to THE hospital. In British English the word accommodation is usually uncountable. Example: There isn't enough accomodation. In American English the word accommodation can be countable. Example: There aren't enough accommodations. You might want to consider these differences as well when you are thinking about an accent.

Which ever accent you think might be more interesting? :)