Your question has no real answer. It's like asking if a 1-inch chisel is sharper than a 1/4-inch chisel. They're both chisels, and they do similar jobs, but they aren't made to do the same job. Furthermore, neither is sharp if improperly cared for. Both lenses are "sharp" optics with plenty of resolution and contrast. As JoeGlo and ronk have pointed out, what you are going to use the lens for and whether it is compatible with your camera body are more important questions.
Without getting into the characteristics of what you would use to shoot with, these two lenses are about equal. If you were talking about the Nikon 105 2.5 MF, I would say differently. The 105 2.5 is one of the sharpest Nikkors ever produced and an excellent portrait length.
I only point this out in case you were confusing the 105 2.5 MF with the 105 2.8 MF. One thing to keep in mind when looking at the Nikon MF lenses: depending on body, the non-AI Nikkors are limited as to the bodies that will accept them. Useful reference for Nikkor lens thread from Nikonians.org.
BOth are sharp. I have both 50/1.8AF and 105/2.8 Micro. Though a macro lens, the 105/2.8 is superb at normal distance, so you can shoot super sharp portraits and even isolate distant landscape. I rarely use the 50s, no matter how sharp they are, they just don't fit my style. Only when you need fast lens for shooting in the dim and don't want to pay extra money for 28/1.4 or 85/1.4 - the 50/1.8 would be an excellent choice. One thing though, the 50/1.8 is sharp for a 50mm, and 105/2.8 is sharp for a 100/105 lens. There's no way to compare both.