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.
As the previous answer mentions, there are certain regional differences within each country, especially with regards to pronounciation.
However, British English often uses 'ou' vowels together in words like favourite and honour. (Like Canadian English)
Often words like centre, theatre, - are written ending with re, instead of er - as is typical of American English.
It is typical in Britain to refer to what Americans call 'movies' as'films'.
British English adds 's' to words ending with 'wards' like: towards, backwards, inwards, whereas American English often omits the 's'.
American English often uses 'z' instead of 's' - as is common with British English with words like: realise/ realize and cosy, cozy.
Where British English spells jewellery, American English spells it as jewelry.
British Englsih - traveller, American English - traveler.
British English often use courgette - the American equivalent is zucchini. British English typically use aubergine, whereas American English use eggplant. However, many of these differences are commonly known by both.
The famous English playwright George Bernard Shaw is said to have said, “England and America are two countries separated by the same language.”
British english are much heavier in sound when spoken.
American english are much softer than the British.