I do not believe the differences are that great. Baltic Birch Ply will not have the voids of standard plywood (which you do want to avoid). The alternating direction of the grain provides dimensional stability and offers stiffness in both directions.
MDF is easier to machine (but the dust sucks!). A good thorough clean up is needed before having drivers closeby, but you should do that with ply as well, just on principle.
BB Ply will suffer water damage better, but hopefully that will never be an issue (don't let your wife use speakers for plant stands...actually that is a damn good upgrade strategy - add a "guilt subsidy" for your replacement speakers!).
In theory, mdf is better because it is homogeneous, but I do not believe the difference is great enough to worry over. BB is solid and not very resonant.
I'm guessing their choices were more manufacturability than anything else.
They may have bought the side panels prefinished and only need to apply veneer to the front and back edges of the ply.
The baffle is not fun with BB because when cutting out the circular holes, you have to worry about cutting against the grain as the router direction changes over 360 degrees.
If you're not sure what I mean, just imagine whittling at the point of a pencil except you have to draw the blade from the point up. The knife will try to get under the grain and you will have little control, and the wood is liable to split or tear-out.