I am starting a build and am not 100% what I will go with. Using ply over MDF would have given me a few more options, but the cost was too high in this case. I will likely use battens, glue and screws. It's true once glue dries, the screws don't do much... but it really helps in glue up, especially if you lack an abundance of large clamps.
The battens and glue should suffice. Construction adhesive if cost effective is OK, but if its much more expensive, you're better off saving a few $$$. Even using PVA wood glue is sufficient, because the glue ends up stronger than the actual wood its holding together. A proper glue joint will hold, and the wood is what gives if there is a break near it. The use of battens will provide more surface area for glue to hold onto, and will therefore be more sturdy if you are using plain sheet goods like MDF.