I have probably 15 old vintage Smith and Wesson revolvers and 7 Rossi revolvers, and generally, the Rossis lock up as tight if not tighter than the Smiths. I just checked the trigger for "waggle" on the .32 Rossi revolver I'm carrying right now, and it's as solid and stable as a trigger can be (and it's from the 1960's...which aren't the quality of the more recent Rossis.)
Smith and Wesson revolvers are better quality than Rossis, generally speaking, but Rossis tend to be good solid weapons, and any gun can leave the factory with problems.
I can't speak to the 971, but I have a 351 (my only Rossi from the Taurus era) and it's excellent. Good luck.