My Father was one of 3 sets of twins. They all went to indies.
His older brothers went to the same school. They were both very bright. They developed a constant rivalry and pupils and teachers kept comparing them to each other. They hated it.
His older Sisters went to the same school and loved it. They were in different forms and the teachers treated them as individuals. Even though they often irked each other before, they came out of secondary school closer as Sisters.
Dad and his twin Sister had to go to separate schools as the choices were all single gender. At first they thought this a terrible deprivation (they were not irked by each other like the other 2 pairs) but after a term or 2, realised they were becoming more themselves rather than one of a pair.
My DH's Mother and her twin went to the same school and were in the same form. They got on well together, but she says they were constantly lumped together.
My Mum and her twin Brother were at different schools because of the single gender issue. They did very well, but Grandpa had always been very clear about treating them as individuals from the word go. They had no separation issues.
So, I think it depends very much on their relationship as twins and on the way the particular school treats them. In particular, being in different forms is important so that they are individuals.
I remember once last year I asked a pupil if anyone was still in the cloakroom. He said "Oh, there's just those little twin things."