I agree that ideally you need to make the decision based on your feelings about the schools and how they fit your child. Your question has prompted interesting thoughts for me, about the decisions we made. Our eldest - choice between place at a pretty academic school, and scholarship at an all-rounder school. Her choice was the all-rounder and we were happy to go with it because they gave us confidence that they were doing thoughtful things to develop and stretch their most academic students. Our youngest, at the school of choice (ours and his), his only chance of a place was via a scholarship. There was also a chance if he did well but didn't get a scholarship, he might be offered a place at that point. At the second choice school, he was awarded a scholarship and they were willing to wait for our decision (several weeks between the two sets of exams). Although it was clear that at that school he would have "stuck out" a bit, possibly even above other scholarship holders, their attitude made it very clear that they would have supported him very well - we ended up making a decision that unless he got a scholarship place at the 1st school, we would accept the second. He did pull off the second scholarship in the end and the more academic school is definitely the best place for him. (to clarify, he's at a boarding school that houses scholars together)
Finances didn't come into our decision making as the bursary levels offered made it a fairly level playing field for us.
I would like to think that most schools would have a programme that would nurture their high achieving students effectively regardless of which ones were awarded an academic scholarship at entry.
I think you have to consider the school's results, less and what they will offer your particular child, more, and whether you have a child who does better "at the top", or responds to being surrounded by an academic peer group. The attitude of the school to your child is also relevant. Any chance to revisit the schools if it truly feels like equipoise on your decision making? Good luck and I hope in years to come you will feel happy about your choice.