Having just done this (state primary to home counties independent), I think it's going to depend on what proportion of the school's year 7 intake come from a state school background. We're at a school with a reasonably large proportion of kids coming from state schools, so they're used to teaching students who aren't from prep school backgrounds. DS was towards the top of the class at primary and seems to be holding his own academically - he's not top of the class, but he's not bottom either, and has discovered an interest in a couple of subjects that he didn't enjoy at primary school, as they're now much better taught. The school have done some rapid recalibration of teaching this year (e.g. in languages), when they realised that a significant proportion of students hadn't covered what they assumed, due to lockdown's impact in the state sector.
There's definitely a lot more sport, though DS is sporty and we're at a school that's known for its sport, so he's happy about that. He did have a wobble with one of the major sports, when it seemed like everyone was better at it to start with, but soon caught up enough to feel he was doing ok. If you know what the school's major sports are, and your DD's never done one of them, this might be a good time to let her try a holiday camp or have a few coaching sessions in it to learn a few basics.
We've not encountered much in the way of snobbery or competition from other parents - they all seem pretty friendly, and freezing to death watching your kids running about a windswept rugby pitch is a great equalizer! In terms of the wealth gap, it probably shows up in things like DH and I both work full-time, whereas some of DS's friends have only one parent who works. Our holiday plans aren't quite as glamorous as some of DS's mates - he's going to a local sports camp this week, while some of his friends are on exotic beach holidays or have gone skiing. However, DS doesn't seem too fussed at the moment. We are planning to put money aside so he can go on a couple of the major school trips that'll be offered when he's a bit older.
The other big difference is quantity of homework. DS has found the transition from the tiny amount he got at primary school to an hour a night at secondary quite a big jump, whereas the kids from prep schools were used to more homework. However, I'm not sure there's really any sensible way you can prepare your child for that! We just made sure DS had decent desk space and a good supply of pens etc. so he can get on with what he needs to do each night.