B.A.
My sister is sending her daughter OS right now and she is going into Kindergarten next year. She is in the before and aftercare right now while going to preschool. I may be wrong but I thought she told me they gradually move them to whole days for Kindergarten to make it an easier adjustment for them. (I can't remember if it was her telling me this or someone else) My daughter is going to a public Kindergarten in another town and they still have naps....my worry is my daughter won't like that because she gave up naps a long time ago. But I think ultimately it will be a good rest time for her.
If it was me, I would probably choose to send all my kids to one school as to not have to worry about sending them to different ones and to keep my child from having yet to start another school all over again. Ultimately though, kids are resilient he should be fine if you go the other way too. Good luck with your choice.