Can I use dense foam board instead of paver base for laying patio pavers?
Who told you that? I'm sure it wasn't a professional! If that was the case, don't you think everyone would use Styrofoam? Sure you can use Styrofoam (polystyrene) but the pavers will be uneven in no time since Styrofoam is fairly soft. Does it get cold where you live? Styrofoam won't get rid of water which will freeze up and heave up your pavers. Plus it will probably void any warranty the pavers might have or installation warranty. 

Paver panels (ez base as you call it) are made specifically for pavers. They are made from polypropylene (a dense plastic) which distribute the weight of each Paver and each step you take. They have channels in the surface to help drain the water away.