I have a Y8 DS at Hampton @LittleOwl22, our choice was also between RGS and Hampton (offers at both) although for 11+ not 13+. DS is really happy there, it is a lovely school. Fantastic facilities and yes the academic pace is fast but plenty of support on offer as well. Loads of extra curricular choice. The biggest compliment I can give is that it feels really down to earth and friendly (teachers, boys, parents). Our DC have all done state primary rather than prep, so venturing into private for secondary can feel a bit daunting, but Hampton feels very comfortable and welcoming.
As others have said journey/distance was a key factor in the choice - Hampton is an easy school bus ride; RGS would have been a more convoluted bus ride, then train ride, then walk from the station. Whilst I know lots of boys love the train journey, and Guildford certainly offers more opportunities for hanging out after school as they get older, the ease of journey to Hampton won out.
Also bear in mind - RGS is very much a rugby playing school, Hampton does offer rugby but is more of a football school. Does your DS have a preference? My DS definitely veered towards Hampton based on a number of factors but football over rugby was definitely one of them!