For me the senior school facilities are much better than prep school facilities. E.g., far more clubs, and I think better-qualified staff, although I am not sure if this is significant.
However, we chose to apply for 13+ because our son is quite immature and would be more comfortable staying in his cosy prep school rather than going to a senior school with 18-year-old adult students.
Our EP also confirmed this - she said she thought it would be better for him to stay where is until 13.
As Amber2 implies, there may be an issue with schools declining borderline 11+ candidates from to-13 prep schools on the basis that they don't want to piss off the prep school by poaching all their kids after Y6. I'm not sure if RGS do this though. I did notice one local prep school's list of suggested senior schools didn't even list RGS as an option, and this is possibly a cause.
In any case I think 13+ tends to be slightly less competitive in terms of numbers to places.
One other factor that we considered was that we felt that the 13+ entry should segue more smoothly from the prep school curriculum, whereas the 11+ entry would be geared towards state school entrants.
Overall if your child is ready, I would definitely start at 11. But ours I think is not.