The 3/4" plywood will have, at most, 1-foot of unsupported span between the cross-beams? It will easily support the weight of the bikes as you roll them across its surface. Plywood is cheaper, lighter, and simpler to attach. Just be aware that the green-treated wood can still warp with moisture. My deck is made of green-treated, exterior grade, wood: I have 2-3 boards that have warped, and need to be replaced -- unsealed, just the green wood exposed, slowly turning gray with time and the elements.
I bought a M/C trailer early this year (ended up with a steel grate surface, no wood needed), and while shopping, I looked at different options, including something like your's. I was planning the plywood route for all the reasons listed above. I wanted a utility trailer, nothing fancy, nothing for show, just functionality. Plywood will give you just that. To dress it up, you can always roll on paint: oil-based, marina/boat paint is the most durable, I believe. Again, cheap can be done, as well, but it will require more attention, sooner.
My trailer has a thick, sheetmetal channel running from front, to back, for the wheels to travel in. This channel not only guides the tires, but it also supports the weight: the steel grate surface is not strong enough, on its own, to support the bike's weight, without bending. You could always fabricate a sheetmetal channel for the tires, with a wheel chock up front. You could even put three channels in place, to carry a single bike up the middle, for best weight distribution. Cheers!
1979 CB750K (sold, 2012, but not forgotten)
1983 Kawasaki 440 LTD Belt Drive (sold, 2011)
1993 Kawasaki Voyager XII