Both are doable, but as Stansted is busier there is more chance of having to wait longer there for your transit or even being refused.
With Stansted the best tip is to listen in on the approach frequency (Essex RAD 120.62) for a few minutes first, before calling them up, to try to gauge the situation -- if there are nose-to-tail transmissions then I'd not bother calling; but if there are good gaps, call 'em up and ask.
In terms of time of day the middle of the day is probably less busy.
They will probably route you via the landing threshold.