Yes! It does mean "B is way better than A". It might help to have some example sentences: "Andy Murray's great at tennis, but he's got nothing on Roger Federer." --> Andy Murray is good, but Roger Federer is much better at tennis A: "Hamburgers are the best!" B: "Are you kidding? They've got nothing on pizza!" ---> Pizza is much better than hamburgers "Superman got nothing on me" (from the song 'One Call Away' by Charlie Puth) --> I'm much better than superman. It also has a second meaning that is specific to police investigations and crime. The phrase is "they've got nothing on me" where 'they' refers to the police or the justice system in general. The meaning is that the authorities have no evidence against you. Criminal A: "Aren't you worried about getting caught?" Criminal B: "Nah, they've got nothing on me." --> the police have no evidence against me Criminal A: "How'd you get away with it?" Criminal B: "The cops had nothing on us." --> the police didn't have any evidence against us. Also whenever I've heard or used it it's usually "A's got nothing on B" where the 's stands for 'has'. "A got nothing on B" is okay too but it's even more casual. The past tense is always "A had nothing on B" (with no 'got' at all).

In a particular context it means A has no evidence against B that can be used to take advantage over B or put B in a difficult situation. You use it very much in a legal way... if someone threatens to put you in prison you can say “you got nothing on me!”

So, for A to have something on or over B would mean that it has an advantage. A has nothing over B means that there's no advantage in any way. So while two things might be debatable in which way to go, this says there's no argument for A at all, and that B is the only reasonable option. It's super colloquial and this is super formal, but I hope this helps.

"A got nothing on B" is not commonly used in casual speaking. If you told me what sentence you'd heard that in, I might be able to help!