High quality MDF tends to be denser, has a more consistent surface quality, and the composition of the wood fibers tends to be finer and more consistently distributed throughout the board. You'll get finer quality cuts (though 99% of the time, you'll want to edge band the MDF anyhow), for example. That said, you don't really go and get a stock list ordered by MDF density (beyond normal and lightweight MDF, anyhow). It's more just a characteristic of the better quality MDF, with relatively minor density differences between brands/product lines.
The bigger benefit is that they're much more likely to stock certified low and no-added-formaldehyde MDF, which make a big difference in formaldehyde off-gassing. Some people are more sensitive to it than others, and the last thing you want is for a beautifully veneered furniture piece to have to be returned because it's irritating the hell out of someone's eyes and nose.