He may not be sporty, but is he competitive? If so, then Whitgift is a good place to be, and he just needs to find his niche be it chess, golf, rifleshooting, debating. It is a school where winners thrive.
Wilsons - the boys obviously get the academic results but far fewer seem to get involved with the co-curricular side of things (unless they are into football!). Also most of the co-curricular activities are provided by external companies. What I think that you miss therefore is the bonding between teachers and pupils which then allows a more mentoring relationship to develop.
I also felt that some of the school-parent correspondence had a slightly hectoring tone to it (based on letters on the school website).
If your son already has some strong out of school interests which you think he will carry on regardless of which school he attends, then Wilsons has to be an attractive option. If you opt for Whitgift then you are in part paying for the increased number of teachers, and therefore the greater influence that you would expect them to have on your son.
Depending on your finances the other aspect to consider is what impact the funding cuts are going to have on local state schools over the next few years. Croydon Council has just scraped the entire school improvement budget I understand. No idea on Sutton's plans, but I can see what a school might want academy status right now.