It’s a great question, but I don’t think you’ll know for sure until you try, to be honest
We stayed on a lovely villa resort last year with great communal facilities. We were doing no parks so we used the facilities a fair few times but my boys (16 & 13 at the time, plus sometimes their 11yr old cousin) were more interested in getting back to the villa pool after an hour or so! However, there were 2/3 of them, and they had a specific game they wanted to play in their own pool, so as you say, it could be different for your boy. I will say that the novelty of a private pool at that age is huge, but then what do the rest of you think? Us adults really enjoyed the resort facilities, it gave the feel of a nice hotel, and we quite like people watching
When we’ve had park tickets and a communal pool we’ve rarely used it as the draw of the private pool, being able to pop inside to the fridge etc has been enough.
The price difference might help you decide too. Happy villa hunting!