I don't know good enought the differences between these two kinds of English (besides civilization against civilisation, color against colour and the like), but for Spanish there is a brief summary:
*Slang is different from country to country.
*American Spanish-speakers doesn't pronounce some letters (s,z,c mainly) as people of Castille in Spain (although some parts of Andalucia in Spain sounds a lot like America).
*The rythm of speakings is very different (but also it's very different from one country to other in America. It's very different in Argentina, in Mexico, in Colombia and so on).
*The main influence of other languages, until very recent in Spain has been French, but in Argentina it was italian, in Mexico it was English, etc.
*The people of America use words that are not common anymore in Spain.
That are a few examples. But all we speak Spanish, and, unless very uneducated, we can communicate between us.
Hope it was useful.