It's really hit or miss with those low end optics. I've used all three, and still have a couple falcons and PA's kicking around. They are great on rimfires... especially rimfires that don't see much action.
I think I've only had 1 BSA, so I can't speak to that one much... but I've had 3-4 PA's and 4-5 Falcon's through here. It seems to be a matter of luck in regard to which has good clicks and functions properly. You can take two of the same scope purchased at the same time, and find that one will be good, and the other is crap.
With optics, you tend to get what you pay for. If you don't pay for it, don't expect to get it. Yet sometimes you can be surprised. One of my PA's is actually quite good! Tracks excellent, clicks are nice, glass is yummy, reticle is clean and straight. If they were all like that, the scopes would be far more appealing! Same thing with the falcon's. I think I have one which is quite good.
So if you have to buy 5 to get a good one... the likelihood of you getting one that's not so good is fairly high. Perhaps BSA has better QC, but I sincerely doubt it.
Still, you can take the BSA or the PA, strap it on a savage 22lr, and you have one heck of a nice cheap plinker for someone to start learning on.