Acoustically, MDF is great. It's made of dust from many fibers bound with glue, so it's inherently non-resonant. But it's not very durable as a piece of furniture. Even if you never get it wet, in humid environments the wood will swell enough that butt joints will show through veneer - you'll see the seams. I think MDF is better acoustically than the best plywood, but it's heavier and less durable.

Baltic birch is much stronger and resistant to humidity. So if your speakers will be moved much or might be in humid environments, you might want to think about that. It is important to use a high quality plywood, which is why I tend to stick with baltic birch. It has more plys that are of higher quality and glued together better, having less voids within the plys. That's the main thing here - you don't want voids. Actually, it isn't the void that concerns me so much as the debris that can be contained in the void. That will cause buzzing. Separated plys can buzz too. Those are the things we are trying to avoid.

If the cabinet you are building is labor intensive or has a fine wood finish, then it would probably be a costly disappointment if a buzz developed and you had to scrap the box. Buzzes can develop years later, when plys separate or debris breaks loose inside a void. Sometimes, if a buzz develops, a small hole can be drilled in the cabinet interior into the section of the wood where the void or ply separation is. You can sometimes inject glue into the hole and repair the damage, fill the void or reattach the plys. But it's probably better to reduce the risk of failure, starting with a high-quality wood to begin with.