I think its quite interesting and completely agree that it depends on the children. I am a twin, and I have twins too, so can hopefully see it from both sides.
My primary school was tiny so there was no option of separating us, and I wouldn't have wanted it any other way, certainly not at that age (4). My sister and I were very close but quite independent too, similar ability etc. Never thought anything of it. We were always together and I loved that.
It never really entered my head about splitting them up when my DTs started school (b/g twins) and it wasn't until we started looking around schools that we were asked a couple of times whether we had thought about it. The general consensus from the headteachers / reception teachers was that they generally advised twins to stay together unless there was a reason to split them (one too dominant / one very shy or whatever). Obviously it depends how the school operates, how you think your children would get on, but for me, unless I had concerns, I'd keep them together. It seems odd to be that you build them up for quite a big step and then send them to different classes without one another. Also as you go further up the school (my DTs are now Year 4), there are class assemblies / parents evenings on different days for different classes / one class had swimming lessons for the first half of the year, one had it for the later part of the year / different projects at different times of the year (requiring visits to museums / local attractions etc, so the logistics of being there for 2 x assemblies etc and the preparation / organisation of doing different things would be hard. Obviously, the well being of your children is paramount but don't under-estimate the practicalities of it all especially if the school is quite keen on lots of parent participation.
FWIW, my DTs have had no issues whatsoever some friends in common, some different. There is another set of twins in their class (2 girls), obviously together, no issues there either. My Number 3 started reception this year, 4 sets of twins in reception this year (60 children). She has one full set and 2 half sets. The other reception class also has one full set and obviously 2 half sets. 2 sets of parents chose to keep them together, 2 opted to separate. I guess its all down to your children.