Neither English variant is inherently better than the other. Personal preferences for the aesthetics of either do not make one more "right to learn" than the other. As Nef suggested, whichever one is more appropriate for a particular individual is likely to be based on which version they are more likely to encounter. If, for example, you think that you're more likely to be speaking the language with Americans, then it would probably be better to learn American English. Either way, you should be able to make yourself understood with anyone who speaks the language, no matter the dialect.
Among the benefits of learning British English is that its usage is more widespread around the world among native speakers. Most commonwealth countries, as well as other nations formerly under British rule, speak a variant of English more similar to British English than American English. In contrast, a preference for American English (or similar variants) is basically limited to the Americas. Thus, if you're planning on using English while traveling, British English might be the better choice.
The biggest benefit to learning American English is probably the ability to better understand American media and culture. If you're a fan of American movies, television, or music, then it's obviously going to be easier to understand their meaning if you're familar with American English. I've also heard it said that 2/3 of native speakers of English live in the United States. So, while British English is more widespread, more people actually speak American English.