I'm an American, but my sister has lived in the UK for about seven years now. She has kept her "yank" accent since she's been there, but she admits that some UKers tolerate the "yank" accent while others hate it. When she's talking to people who hate it, then she "tones down" the American accent.
Since she's told me there there are actually dozens of English accents in the UK, I assume that when she changes her accent she's actually changing it to be closer to Received Pronunciation. Is this the accent that is taught as "Standard British English" to students in other European countries? I wonder.
At the same time, I think the majority of Americans would find an "English accent" to be charming and melodious.
So I think the question of "which one is better?" really depends on your audience. You should first strive to be understood, then strive to impress (or, at least, not offend).