Acrylic is probably the most strong, it does not crack and is pretty tough to chip. I have dropped my call on concrete a few times and it has never chipped. Acrylic has a loud, fast, sharp tone to it.
Polycarb calls are loud, inexpensive and will kill ducks. I have found my polycarb calls seem to chip or crack (maybe I have bad luck)...
Different woods have different sound and strengths. Cocobola is dense and fairly loud and has lots of oil which helps to keep the call from getting damaged. There is just something about wood calls I think the ducks like. You hear a lot of old guys talk about how a wood call sounds better the wetter it gets, meaning as you blow it throughout the day. I used to blow a faulks wood call that was only $6 that killed a ton of ducks, it was ugly a sin, had electric tape holding it together, had no finish left on it. I bet the guy who found that in the field I lost it in didn't even know it was a duck call. lol
Wood is a lot cheaper, you can pick up a RNT cocobola shortbarrel for $80 vs Acrylic for $130. Sometimes you can pick up good wood calls used from a guy for $50 that usually cost $80.
They both have thier place IMO, my next couple calls will be wood calls, specifically a cocobola shortbarrel and a wood Timbre. I also have my eye on a DOA double trouble for some softer calling....
Mike