We have had this choice twice now - older DC picked Hampton over RGS and youngest (just done 11+) will likely do the same. The two are very similar academically, both lovely, we know very happy boys at both and you can’t go wrong with either! But FWIW this is what we based decisions on:
Travel - ease of journey as others have said. Coach to Hampton is easier for us and shorter overall journey than train to RGS - though worth noting the expense of coach and fact that we are completely reliant on it. In theory the train is more flexible and far cheaper BUT also bear in mind train strikes, if you’re reliant on train.
-Links to girls school - as an all boy family we like the fact Hampton has a link with LEH, the boys socialise a bit with LEH girls on the coach etc and there are some shared activities (but again RGS boys would get that with GHS girls)
-Sports -RGS is mainly a rugby school, Hampton mainly football (neither of my DC like rugby). Hampton also offers rowing (shared boat club with LEH) which older DC loves and younger DC keen to try.
-Setting - RGS is a town school, Guildford is lively and buzzy, far more opportunities for socialising after school as DC get older. But this does mean their sports fields etc can’t all be on site. Hampton has all sports fields on site but is essentially suburban -literally one little newsagents round the corner from the school! My DC are more comfortable with suburban rather than urban so they are perfectly happy with this but others might find it limiting / claustrophobic.
As I say - can’t go wrong with either but the above formed the basis of our decisions. Hope that helps and good luck!