Depends on you. Whichever sound/feel the best to you.
FWIW, I've used Ernie Ball, D'addario, SIT, DR, GHS, Thomastik Infeld, and Dean Markley, all in gauges ranging from 9-42 to 18-80 with Floyd trems, and none was so better/worse that it really made a difference. Overall, SIT is my favorite, but I could use any of them and be perfectly happy.
I've got 9's I think on my SL3 (I never put them on they came with the guitar, but they feel like 9's).
The RR3 has Ernie Ball "Skinny Top Heavy Bottom".
THe Floyd works fine on both. I wouldn't worry about it - use whatever ones you like best.
In my experience a Floyd Rose system doesn't need any kind of different strings than any other bridge option on electric guitars. Just go with the brand and gauge you feel the best. Try different strings out every now and then, you'll eventually find your favourite.
I don't know man, I had a 10-46 set on my FR guitar and I had to put one extra spring in there. It turned out to be way too stiff. 9-42 rawks :approve:
D'Addario ProSteels 9-42 are the best strings for a Floyd Rose. If anyone wants to disagree - there is a stash of E-Punches I've been holding back on for such an occasion.
Brand and gauge are irrelevant, although as pinto said lighter strings cause less pressure on the knife edges and thereby prolong the llife a bit, but it´s not something you´d notice until after a few years unless you´re a heavy trem abuser. I use 12-52 , 13-60 and 14-70 and have no issues, but my axes are also professionally maintained and always ready to rock at the drop of a hat Someone who takes a bit less care of their instrument may also have minior issues, though I´m not aware of any that aren´t directly setup related
My standpoint as a luthier: Always choose strings for tone and playability, which of these is the higher priority is of course your decision. Because if the axe sounds or plays like crap in your hands then no "perfect string for such and such piece of hardware" is going to solve that
PS: of course different guages will cause a slightly different trem feel, especially above 10s or under 9s where adding or subtracting a spring may be necessary to compensate for the tension difference