In case you can’t tell, I hate MDF. It’s a necessary evil if you want the really smooth surface, especially if you get the melamine-faced material often used for kitchen cabinets. Every time I use it (for jigs and such), I end up wishing I had splurged for hardwood plywood.
It’s about 25% heavier than hardwood plywood, perhaps more like 50% heavier than softwood ply. It’s sort of homogenous and isotropic, except that the manufacturing process (pressing fibers into sheets) means that it’s not quite as dense in the center.
Unless it’s made with an exterior glue, it tends to be a sponge for finishes or spilled liquids. It also tends to chew up tools, even with carbide-tipped blades and bits.
In terms of strength, it tends to suffer compared to plywood, especially when density is factored in. The Hardwood Plywood and Veneer Association claims that it’s stronger than steel pound-for-pound – remember that they used to make airplanes from really high-quality plywood. You can buy aero-grade plywood, I believe, which has many more layers (the “ply” in plywood) than regular construction-grade material. If you want extreme performance, you can even make your own plywood (or specify it for someone else) with special orientations for the layers – instead of alternating 90 degrees between plys, you can set up 30-60-90 layups with somewhat different directionally dependent properties.
In fact, given aluminum’s many shortcomings (relatively poor strength/toughness in many alloys, weldability, etc), I personally think that you could make a pretty darned good robot chassis with high-quality plywood. (If it was good enough for Howard Hughes and the Spruce Goose…)
Besides weight, MDF tends to have creep (or “set”) problems. Under load for a long time, panels will develop permanent bends. Plywood does this as well, but not nearly as badly. If you’re used to materials like steel and aluminum (at room temperature), this can cause real trouble for critical structural components.
If you have to use it, consider trying to find a big MDF wholesaler who will have the less-common varieties with reduced weight, increased strength, exterior glues, etc. The big box stores all sell the same cheap stuff, but if you can find the right source, you can address specific shortcomings.
In short, it’s cheap, heavy, absorbent, and has good surface/dimensional consistency. Unless you really need one or more of these properties, you’d be much better off with solid wood or plywood. Wood and wood-based composites (plywood) are often quite competitive with high-tech materials like graphite/epoxy or fiberglass-reinforced polyester.
Way more than you wanted to know about wood as an engineering material:
http://www.fpl.fs.fed.us/