The big advantage of receiving passes with the "stiff" method is that you kill the spin of the puck, which prevents the puck from rolling off your blade. I find that with the "cupping" method, I have to worry about losing the puck.
There are some other pros. With the "stiff" method, when you receive the pass, the puck will be in the ready position, rather than slightly behind you as with the "cupping" method. Moreover, because the puck stops right away with the "stiff" method, you are in a position to quickly execute your next action, whereas with the "cupping" method, there is the lag time from having to cushion the puck. The "cupping" pass method might work better for a soft pass, but in a game, you should always be throwing hard passes. So it seems to me that the "stiff" method wins over the "cupping" method in all situations.
The only caveat is that I've only tried this out with my composite blade. The results may be different with wood blades.
Apparently, I'm not the only one who has made these observations. This webpage says basically the same thing.
Incidentally, I've been told (on the ModSquadHockey forum) that killing spin also plays a major role in successfully catching backhand passes. A condensed version of the discussion:
A good way to cheat it so that it's easier to receive a pass is to angle the top of your blade towards the puck as radio mentioned.
/ for rh
\ for lh
and try to catch the puck around the bend from the hosel to the blade, before the curve starts.
If you angle your blade that way, you kill most of the spin that's on the pass, which plays a major part in why the puck flies off your blade.