I have had a few Mosins that had the "sticky bolt syndrome", which is fairly common thing for new owners to encounter. As I understand it, it is from varnish from left over cosmoline getting baked into the chamber. Typically you can do a very through cleaning and reduce or eliminate the problem, but I remember one particular gun that I could never get to work smoothly. I never had this problem with any Mauser rifle I've had.
Accuracy depends on the rifle, but I don't think you could say one is particularly more accurate than the other. Some Mausers are more accurate than other Mausers, and some Mosins are more accurate than other Mosins. The 7.62x54 Mosin round is a more ballistically efficient round, so for distances it may be more accurate. The 8 mm round is slightly larger, so potentially more power for shorter distances, but I think for most rifles either will be more accurate than the shooter. With the Mauser you also can find a lot more caliber variations. 6.5mm, 7mm, 7.65x53, etc.
The Mosin will tend to be cheaper, so you may be able to buy 2 or 3 for the price of a Mauser, and get one really great shooter out of the batch.
If you are looking for the most accurate Mauser, consider a Swedish Mauser in 6.5 mm, or possibly a VZ 24 in 8 mm.