I'm afraid it isn't that simple. TV stations have to run at a single frame rate and resolution - and BBC HD is 1080/50i. The transmission area - vision mixers, graphics, servers, outside sources, VTRs (if still in use), studios etc. all run at the same resolution and frame rate. It simply isn't possible to switch frame rates on a per-programme basis.
Whilst all HD Ready displays can accept 1080/60i - it isn't feasible for the BBC to broadcast in it.
AIUI the SD feed on BBC Two is a 576/50i downconversion of the 1080/50i being broadcast on BBC HD. The conversion from 60Hz to 50Hz is done in the HD domain - so any conversion artefacts will be common to both?
I guess there may also be an SD backup from the US as well.