Irena is right, "gotta" is very casual and informal. Its a made up word used in pace of "got to". "You have to" is more more formal but can be used anywhere even informal settings because it's grammarically correct.

you gotta= its necessary you have to = you must!

Written with 'have' or without it, 'gotta' is very casual, and should only be used in informal conversation. It is considered to be grammatically incorrect form .The equivalent and more formal form would be, 'I have (got) to' or 'I've got to'.