As far as I know, "lots of" seems more informal than "a lot of" (But they are less formal than "many" and "much"). However, I see people often use both of them without too many differences.

1 The expressions a lot of and lots of are used before nouns to mean ‘a large number or amount of’. In common with other words denoting quantities, lot itself does not normally function as a head noun, meaning that it does not itself determine whether the following verb is singular or plural. Thus, although lot is singular in a lot of people, the verb which follows is not singular. In this case the word people acts as the head noun and, being plural, ensures that the following verb is also plural: a lot of people were assembled (not a lot of people was assembled). 2 A lot of and lots of are very common in speech and writing but they still have a distinctly informal feel and are generally not considered acceptable for formal English, where alternatives such as many or a large number are used instead. 3 Written as one word alot is incorrect, although not uncommon.