Birch Pros (13 ply birch not the ****** kind)
Light weight, easier on tools, can be stained nicely, and less dust.
Cons
Can be 2-3x the cost of MDF, if you do not know how to cut it properly the veneer can come off
MDF Pros
Cheap, easy to sand, did I mention cheap?, very dense.
Cons
HEAVY!, The formaldehyde laden dust is horrible for you, Hard on tools, can split easily
If you want the best of both worlds Trupan Light or MDF Lite will be the best between the two in terms of lightness and density.