The usual, or most common advice, is to try and keep things in balance, i.e., what goes on one side should be pretty much repeated on the other. I think it's well known for example that veneering one side of a panel without some sort of balance veneer on the other side (not necessarily the expensive show species on the 'money' side) leads to cupping.
In theory therefore you ought to wax both sides of your panel. However, wax being what it is, it provides little in the way of protection against water vapour passing through the finish to the wood (or MDF in your case), so I suspect you could get away with waxing just one side. A finish more likely to cause imbalance would be a decent film forming polish, such as pre-cat lacquer, oil or water based varnish, etc because these can cause cupping on their own just because of the film thickness having some structural integrity, much greater than wax anyway. Also film forming finishes more effectively slow down the movement of water vapour into and out of the wood below, whereas the other side might be more exposed to the adsorption or desorption of water vapour.
Set against all that are the numerous panels I've seen finished on just one side, primarily old and antique furniture, cabinets of various sorts for example, drawer fronts finished only on the show face, etc. Frequently such structures have been fine, but that's in part because the drawer fronts, for example, are restrained at either end by the drawer sides. Larger cabinet parts such as sides are relatively well insulated from external changes in atmosphere because a cabinet that's opened infrequently creates its own relatively stable internal micro-climate, and the finish on many old pieces of furniture are things like linseed oil and wax, neither of which form much of a barrier to water vapour anyway.
In your case, you could start by waxing just one side, but if the panel cups either right away or some time in the future, you could apply wax to the other side to see if that reduces or eliminates the cupping. On the other hand, you could just wax both sides anyway, although you may have good reason not to, e.g., the unwaxed side might be fixed firmly to some sort of supporting framework. Would it be a big task just to do both sides, or is there a good reason not to do so? Slainte.
