Here are my thoughts.
Hampton is bigger than RGS, but it is on one site.
It is more expensive.
Hampton:
Fees: £15,255
Lunch: £756
Coaches: £975
Total: £16,986
RGS
Fees: £14,070
Lunch: £690
Season ticket from say Effingham: around £500 per year
Total: £15,260
Which is a little over 10% more.
Plus I get the impression Hampton put on more trips, which you may see as yet another unwanted expense, or a fabulous experience for your child.
My impression of Hampton was that it is more modern/forward-thinking, e.g., they seem to be more interested in the use of IT in education, and I believe RGS had no SENCO prior to 2 years ago, whereas Hampton have a dedicated department and a range of courses/screening:
www.hamptonschool.org.uk/The-School/Academic/Learning-Support/Extra-Page-(3).aspx
www.hamptonschool.org.uk/The-School/Academic/Learning-Support/Learining-Suppot-Doc.aspx
which they will happily add on to your bill! But it would appear better if your child has weaknesses that they IMO seem better able to address than RGS.
RGS seems to be relatively more singular about maths and science:
www.rgs-guildford.co.uk/page_viewer.asp?page=A2+Results+2012&pid=472
www.hamptonschool.org.uk/The-School/Academic/Exam-Results/Results-Table/A-Level-Results-2011-(1).aspx
whereas the second-most popular subject at Hampton for A Level is History.
I spent some time in conversation with the head of maths at Hampton and was very happy that they would stretch in this area, certainly their website supports this:
www.hamptonschool.org.uk/The-School/Academic/Academic-Departments-(1)/Maths.aspx
Hampton has improved out of proportion to wider grade inflation, e.g., in 1997 they got 53.5% A*/A at GCSE, at RGS Guildford in 1995, the figure was 73.4%, now both get ~90%.
RGS has a better record of Oxbridge entry, sending a quarter of the sixth form there each year, for many years: www.rgs-guildford.co.uk/page_viewer.asp?page=Leavers%27+Destinations&pid=405
Hampton School has never matched this, but this year sent 32 to Oxbridge,, which is close to 20%. The previous year, only 15 went to Oxbridge.
The Hampton head has said that with their now stellar results they have become more selective and expect to improve their Oxbridge stats.
You pays your money and takes your choice, DS preferred Hampton because they taking rock climbing seriously, which is very unusual - RGS do not.
Obviously I'm bitter and biased, DS having been rejected by RGS, btw.....