What is a "British" accent? There are so many very different accents - remember that Britain includes Wales, Northern Ireland and Scotland. Some parts of Ireland and Scotland have beautiful, almost musical accents. I come from Australia, but I'm not very patriotic - they have a horrible sound! Pronunciation is the most important - accent is just the sound, like the difference between a piano and violin. Be proud of your own accent!

I do think both are equally good, and it really depends on your personal goal, whether you want to go to UK or USA. If you want to go to UK, then go for British accent because it's more relevant and you'll hear it everyday there. Same goes to American accent. This is also related to personal interest. Some people prefer British accent and the others prefer American. Go ask yourself about this. And like Simón said, there are so many different accents in English. It's not only about British and American. There are Australian, Canadian, South African, and more.