I also have boy/girl twins. They are in the process of sitting the 11+ and I have deliberated over the same issue as you. My DCs are in the same class at primary school but are very independant of each other.
Their decision was they would prefer to be at the same secondary school but were quite happy to be at separate schools. This fitted in with what I would have guessed. We are therefore applying for 2 co-ed schools and 2 single sex schools on each CAF.
I don't think there is a definitive answer. You have to look at your own children and your family situation ( difficulty of managing different journeys to school etc)
My main headache is the worry that one will pass the test and the other not but you won't have that problem if you're going for indies.
Good luck. There are many joys to having twins but also some problems that you don't forsee when you find out you're having twins