But are there any drawbacks to poplar?
It depends on your design, and if you can get POPLAR PLYWOOD from Lowes. I've never seen it there OR at Home Depot type places. Although it IS available. Cheap too for the right product. Actually, I work in a custom cabinet/woodworking shop, and use a fantastic 3/4" Poplar Ply from China. $27(my price

) per 4x8 sheet. This stuff is ELEVEN PLY, with NO voids, great color variations on the face plys, with a very pale whitish overall color with streaks of burgandy/red through it. Unfortunately, this does not match solid American Poplar if you needed solid stock edgebanding or face frames. Although you could double bevel the ply or slice(rip) the face for edgebanding if so desired, but again, it depends on your design. Solid stock comes as a greenish color with streaks of brown to black through it. The green color will change though, if exposed to UV rays from sunlight. It turns it brown with even slight exposure. Even with a clear finish.
But if you are talking glueing up solid stock to form panels for the sides and or decks, you are looking at a ton of work leveling the panels, unless you have a widebelt stationary sander available. Takes lots of long clamps as well. We do this all the time for raised panel doors etc. And since Oak ply and solid stock is redily available, and isn't THAT expensive, I'd stick with the oak. Although one other thing is good about Poplar. Because it is a closed grain, it is the best wood for painting. Oh another thing about the ply. Because the Poplar ply I use has so many plys with no voids, I simply USE the exposed plywood edge. Looks great with a clear finish. You could do this with Oak ply as well. I do it all the time.
Where you get into a problem is if there's a lot of voids in the laminate
Cabinet grade ply has no or very small voids. You also can get it in ARMOR CORE too, which is plywood with an 1/8" ply of MDF under the face veneer which keeps it absolutely flat. Typical oak ply will telescope inconsitancys of the interior plys to the face veneer, such as knots, voids etc. Check the face for loose and or thin veneer and SAND THROUGHS from the factory. This veneer is typically only 1/42" thick
Oh, I forgot. Oak can be found as a veneer, and as a veneer on 3/4" MDF, although it is usually not as redily available to consumers as plywood is.