The difference between an RS and a R3 are:

R3 has 1cm shorter chainstays
R3 does not have curved seat stays
R3 has a shorter head tube.
R3 is very slightly (like 75-100g) lighter.

It is not going to be measureably faster up hill. It might be slightly faster on the flat IF you take advantage of the shorter head tube and set the handlebars lower.

If you climb better with the lower gearing, put a compact on the KOM.