Neither American nor British English are themselves uniform, containing many regional variations. To compare American and British Englishes, it is probably best to select the two parallel formations of Standard (Edited) American English and the British Received Pronunciation (RP) or "BBC English". Differences can be located on levels of spelling, pronunciation, and word choice, inter alia.
Spelling: British English uses "re" where American uses "er", as in theatre/re; centre/re; etc. British English uses "our" where American uses "or" as in honour/or; flavour/or; colour/or.
Pronunciation: In British RP, stresses tend to be more regressive (falling on an earlier syllable in a word) than in American.
Word Choice: Many specific words differ, e.g. articulated lorry/truck (18-wheeler, semi); petrol/gas; sit exam/take test.