This is really raw advice and could differ from board to board: Poly is said to be the highest performing because of the way it flexes and is used by pros because they are sponsered and don't have to pay for the new board they get every day. Epoxy is harder to ding and will last longer the poly, but the performance is sacrificed a little, but unless you're a pro, you'll barely notice the diference. Just make sure that you don't buy and epoxy pop-out, (pop-outs seem to favor cheap plastic-like epoxy that really shoudn't even be allowed in the water.)
Epoxy or Poly then you surley mean Resins? If you are buying a fish off of the rack, good chance it's epoxy. Remember, you are not buying a fish for hi-performance types of surfing. You can rip a fish to death, but the fish is generally ridden differently in my perspective. In reality you can get a big-ole-thick fish in wood, epoxy, polyester, surf tech, aviso and may more options and they will perform so simliar that the issue then relies on the fin set up and dimensions more then anything else. For this type of board, get what feels good in your hands and that will function correctly for you. Don't worry about what it is made out of as long as it's a reknown shaper, or someone trustworthy of their craft! If you want a shortboard and have money (and that you not ask)...poly it is!
Check out Firewire Surfboards. You kinda get the best of both worlds with a stringerless EPS blank thats vacuum bagged in a epoxy shell and that has parabolic balsa rails. Besides being super durable the flex is amazing. What sold me was the guy at the shop flipped upside down, stepped on it and pressed it to the floor.Try that with a poly and you'll have broken or flex cracked board. I bought a 6'6" tri but they have a full line of shapes. I gave mine a good workout in Nicaragua and the spring and snaps out of turns was amazing. I have plenty of poly boards and love them but I think the Firewires are making the best new technology style boards. Good luck!