OK, so, I have no figures and numbers and academic comparisons for you but here's some basic things about the (non academic) differences that I have observed.
In Switzerland (assuming you and your other half speak English at home) your kids will grow up bilingual - properly bilingual - and perhaps with even more languages - which they probably won't in the UK where languages are taught as academic subjects much later.
Kids start school at an early age in the UK, and are taught reading, writing, maths much earlier. Here they don't start that until 7 years (primary school age here), but I'm told things basically even out around 9 to 10 years of age.
Kids go to school longer hours in the UK and have lunch at school - here they get sent home for lunch and are not at school most afternoons (until quite a late age anyway). Schools in the UK pretty much all cater for the 2 working parent scenario with after school and before school care options, here they really don't at all (although this is changing slowly in some places).
Most UK schools have a uniform, here they don't.
In the UK not all schools are equal and with the publishing of league tables there is a lot of competition for "good schools" - so you may not get a place at the school closest to you, or one that you want. Here all schools are pretty much equal, there are no league tables or results published and you will definitely get a place at the school closest you whether you like it or not.
In the UK nearly every kid is driven to school by their parents. Here, everyone walks to school (or rides their bike/scooter) on their own from age (around) 5. Normally this is because school is much closer here!
One huge advantage of having your kids grow up in your home country though is that you at least have a basic understanding of what they are going through - even if you were at school a lot of years ago (like me!) you will still understand what English school is like. And how things like "assembly" and "show and tell" work, and what's expected of you as a parent. What consists a "sports kit" and what sports they might do. I really struggle here with knowing a lot of things that are totally obvious to Swiss parents e.g. the first day at school - I had no idea that there was a big ceremonial party type thing with songs and welcome gifts and other stuff for parents and kids - in the UK you would have dropped your kid at school, perhaps said hi to the teacher and then left straight away and as soon as possible!
At the end of the day I think it's probably better if your child completes their education in one country - switching is always going to have difficulties of one kind or another (big, small or unknown), and for the kids a stable life where they know where they are and will be in the future is important - in terms of happiness and friendships at least (and these are important to kids). The exception of course being if your child is deeply unhappy at school - then it is probably a good idea to move!
I know where you're coming from though. My son has loved his years at Kindergarten and his first 2 weeks of primary school. I on the other hand have found it more and more complicated and confusing and wishing that we were going through all this in the UK where I'd have a much better clue about how things work. But I have to put him first - he is happy and is doing brilliantly, and as a parent, that's what's most important to me.