Personally, I think that unless you are going to a 13+ school where everyone or almost all start then, it’s better to go at 11+ and begin with the majority.
13+ preps are struggling in yr7 and 8 unless they send most of their kids to 13+ schools - and there are fewer if those these days, now most of the day schools take in at 11.
Some 13+ preps have abandoned doing Common Entrance because the curriculum felt old fashioned and dull and didn’t replicate what the kids would be doing if they were in secondary. With pre-tests in yr6, very few schools,especially day schools require CE. It offer based on their own 11+ gets even for 13+. So on that basis, CE just is t really needed for most these days.
I also think it’s a different experience to be in Prep rather than Senior in yr7 and 8. There will be specialist teaching in the Prep but it’s not the same as having secondary teachers who teach A Level etc. Facilities can be good, but again unlikely to be the level of the senior school. And for me, most importantly, I’ve seen those in Preps feeling like they are left behind and just waiting - especially when they hear from kids who are in yr7 and 8 at senior schools and especially the school they will go to. They can feel they are missing out in friendship forming, being up to speed with the work and it can be really hard for the Prep to keep them motivated, especially when they already have their places based on pre-tests and aren’t reliant on the work they do in yr7 and 8.
Ive heard it said before, it’s best to enter any school at its standard, majority entry point, in the vast majority of cases. There will be exceptions such as those who will benefit from a smaller environment or who aren’t ready for senior school yet, but most are ready at 11 and if that’s when most will come in, I’d send most children then.
It’s a shame for 13+ Preps that don’t mostly feed boarding schools. I think they are fighting the tide really and even in the last 5-8 years, many have struggled as the appetite for 11+ and getting a place sooner rather than later, and senior schools take in at 11 when they either didn’t before or only took small numbers, change the landscape. There is something lovely about being the top of the school in a Prep at 12/13 and getting leadership opportunities etc, but I do think they miss out and when they join the senior school, it’s much harder to break into established groups and hit the ground running with GCSE study, if you haven’t familiarised yourself with the ways the school works etc through a more gentle start in yr7 and 8.