You should probably do some sort of matrix / chart to compare the options, and also try to establish what are your priorities. I always find that getting thoughts down on paper when trying to rank options really helps.
Ultimately, it depends upon what you feel the benefits of a private education would be - and whether they would be worth the cost to your family. What scale are the scholarships? Are they eg 25 %, or higher?
For us, as a family (we have 3dc), paying for private school would probably have been impossible for all three (perhaps possible for just 2 of the dc); so accepting a grammar school place for dc1 (and subsequent dc) was definitely the best option for us. It has meant that we have avoided the financial pressure, so now have the funds so that our dc will avoid any student loans at uni, and then we hope to help them further down the line when it comes to contributing to housing deposit - which I doubt we could have done had we stretched massively to do the school fees. We also managed to overpay our mortgage over the last 15 years, so we are now also mortgage-free. Which we couldn’t have done with school fees.
For dc3 (when making the grammar v independent decision), dc3 asked how much it would cost to send them to private school for 7 years, and was absolutely aghast when we said it would be approx £175k. Dc3 then said - actually I’d prefer to have that money to go towards a house, please!
We didn’t have the option of scholarships (very well done to your dc for that!), and your financial circumstances may be completely different to ours.
I have a friend whose dc went to a very selective, independent prep school, and discussing options with them over the years, I was surprised to hear that the majority of all dc at the prep tend to go onto independent secondaries - so it seems to be almost a given that dc would stay in the independent sector.