IGA also makes a side by side. It's imported by Stoeger. If you look around, you might be able to find a used Rossi coach gun, with genuine external hammers. <drool>
I have the IGA, so I can't comment on the EAA, but for a play gun (and that's all my IGA is), it's perfectly good. The triggers have a LOT of creep (double action shotgun?), but they're fine for CAS.
SASS rules limit the pumps to 2 rounds, so from my POV, any advantage lies in how fast you can reload it. Some of the more serious competitors hone the chambers of their doubles slightly oversize, so the hulls fall right out. They seem to be on par with the pump shooters. Those of us who have to claw the empties out of our doubles seem to be at a disadvantage.
Since I'm lazy, the big advantage of a double for me is easy cleaning. Couple of passes with a bore snake and it's done.
Keep in mind, not just any pump will do. It has to have an external hammer, and this means the 1897 (I think) Winchester. I've never priced these.
Before you commit to either type, you should make contact with your local group. There will always be someone willing to share guns for a match, provided you supply your own (factory) ammo.