When it comes to durability, plastic wins hands down - it'll easily last 20-30 years, whereas MDF degrades faster, especially in the kitchen because of moisture and temperature swings. MDF will warp, swell, and the paint will start peeling. Don't use MDF for the kitchen at all, honestly - it just won't hold up there.
Appearance-wise, it's trickier. MDF looks more elegant, does a better job imitating wood, holds paint better, and veneer sticks to it just fine. Plastic looks like plastic - cheaper and more obviously plastic-looking, though there are some decent-quality models out there. Plus MDF is easier to repaint if you decide to redo your interior down the road.
Installation is pretty similar between the two, but there are differences. Plastic is simpler and faster to install, and you can hide cables more easily through cable channels. MDF needs a bit more care - you need to cut it more precisely, and dealing with joints is more of a hassle. If it's the kitchen, go with plastic even though it looks less fancy. For a living room you can take a chance on MDF - there's less moisture there and it'll last longer.