We see a LOT of 51's and 55's with P/C troubles simply because of the shear numbers of them still in service. They are/were a very well made saw, and priced right, so they sold a lot of them. They remained popular because they have a good power to weight ratio, and were reliable in long term service.
Eventually, someone will forget to put some oil in the fuel, or allow the saw to operate a bit lean, etc, and the result will be piston/ring/jug troubles.
I bought our 55 off of E-Bay for under $100, and it was nearly mint condition, with a very small amount of aluminum smeared over the piston ring. I cleaned up the piston, ring, and jug, and had it running in about an hour without purchasing a single part.
As soon as I got the saw running, I noticed that it was set quite lean at WOT, and probably what led to the troubles in the first place. In any case, I added some fuel with the "H" screw, and it's been running flawlessly ever since.
I just bought a 51 about a week ago, and it was still running fine, but in HORRIBLE shape as far as dirty/grimey and poorly maintained. It is a 1999 model and the carburetor had limiter caps on it. It was also WAY too lean for my liking, so I richened it up some. I would imagine a lot of the later models were set pretty lean to keep the EPA happy, which may also be part of the reason we see a lot of them with smoked P/C's?
As far as parts swapping, the 51's and 55's share just about everything (at least the later models like I have) not sure about the 50's?
I've also heard that 55's were made with closed and open transfers, but I have no idea how to tell which is which. Our 1998 model has closed ports......Cliff
