"You've got to" is similar to "you need to". They're basically the same in meaning. However, "you've got to" is more common when talking about general qualities that you need in order to achieve a certain goal. For example:

Most importantly, you've got to be passionate about it.

If you want to get into an Ivy League school, you've got to have impeccable grades and an impressive list of accomplishments.

"You need to" is more common when you're actually telling the listener what they should do, right now.

You need to go talk to Mrs. Green about that.

You need to stop spending so much on entertainment and put some of that money toward your savings.

"You need to" also sound more angry.