BRITISH ENGLISH IS BETTER!
All joking aside, in terms of grammar etc. there are no major differences, there are slight differences in spelling. e.g. color (US) and colour (UK), fuelled (UK) and fueled (US), centre (UK) and center (US), etc. and also differences in choice of words such as on holiday (UK) and on vacation (US), pavement (UK) and sidewalk (US) but not to the extent that a British person wouldn't be able to understand an American or vice versa.
In terms of regional accents, I think American accents overall may be easier to understand than British ones (my opinion as a Brit), as British accents do vary quite a bit despite only being a small country. In the UK not everyone speaks Queen's English and many people struggle to understand northern accents when they first come here. However the deep south American accent can also be quite hard to understand (even for native speakers).
I guess at the end of the day there is no real definitive answer to your question. I would honestly say just learn English, and you'll naturally pick up on the differences between regional varieties.