Happy to share our experiences too.
Applied to and got offers at 3 private schools for our son, but only because we'd been through it already with our eldest so knew more what we wanted and location was important. Still, it didn't stop us changing our minds as we went through the process!
Really liked the down to earth feel (for private schools) of Hampton and KGS. Hampton used to be a grammar school and still has that feel about it. Eldest is at KGS and they couldn't be happier (great school, lovely community), but they don't do rugby which is my son's favourite sport. Despite really loving it. Hampton was too far in the end as we had offers from other great schools far closer. Didn't apply to St Paul's as the fees are a step up in later years and we couldn't see the point, plus we wanted to head / point away from London (albeit not that far!), if that's makes any sense?!
In the end it came down to Kings and Tiffin, and we chose Tiffin after going through all of that! Almost a week in and our son is very happy there and has become 'bus buddies' with two other boys from near us and is going to another boys house after school this week.
In contrast to the poster below, my feeling is that lots of boys are good at maths, but English sets them apart, but that is only my view from what I noticed from our son's experience and from others going through this, but I could be wrong. KGS aren't doing verbal reasoning this year, so it may make it easier to get in ( it can be tricky, also because it's co ed so competition from girls) as that has apparently previously tripped a lot of kids up according to parents.
Advice would be go for an easy / quick journey. All these schools are excellent and these kids will be shattered at the end of the day and getting up in the morning. Also think about where the sports fields are for weekends and how easy to get to for parents' evenings etc. This was a reason against Hampton, but only because of where we live. Personally, I also preferred independent travel with good transport links rather than being on a coach for years, but some kids really love I being with their friends on the coach (but you can get the same thing on a public bus... and it's free!).
Happy to answer any questions.