'Pretty' before an adjective means 'somewhat, fairly, moderately'; it is less frequent in British English, where you are more likely to hear 'rather'. 'Quite' has different meanings in British and American English, so you need to be careful. For example, in a restaurant, in response to the question, "How was your meal?" American: "It was pretty good." ( = rather good, fairly good, moderately good, above average, but not great) "It was quite qood." ( = very good, extremely good, excellent) British: "It was rather good." ( = fairly good, moderately good, above average; or sometimes, surprisingly good) "It was quite qood." ( = not great, mediocre, just so-so, it left a lot to be desired) and this meaning becomes even more negative if the word 'quite' is stressed. Be careful! A British chef will be offended if you say the food was 'quite good', because in British English this means that it was just mediocre, whereas in American English it means that it was very good indeed.

Both these words are used to describe considerable size, quantity, number, extent or degree. For example, you could say, "It looks quite big" or "It looks pretty big". However, using the word, PRETTY is considered informal. I wouldn't recommend it for a written or formal conversation.

Both words can be used as adverbs, while pretty can be used as an adjective. As an adverb pretty means to a moderately high degree. Quite means to the utmost degree. So, quite is the stronger of the two words. "Pretty sure" would imply that you were certain with a high degree of certainty. "Quite sure" would imply that you were certain with a very low degree of uncertainty. Pretty can also describe the way a person looks. Pretty would be used as an adjective more often than the adverb in formal situations.