i'm going to take it you mean athlon 64 (such as venice, san diego cores) vs. opteron single core series (opteron 146, 154, etc.) or amd x2 (3800+, 4400+, etc.) vs. opteron dual cores (opteron 165, 170, etc.).
I dont know a whole lot about the single cores, so i'll say what i know about the dual cores...but i'm sure the difference is the same with the singles as with dual cores. amd athlon processors are made more for consumer use, while opterons are made more for servers or workstations. They both perform quite similarly, but the opterons have a slight edge because they usually have a larger L2 cache. The opterons are made and tested to be able to withhold constant cpu-intensive loads (since they are for workstations), and are therefore built a little bit more 'hefty'. for instance, the memory controller is of a slightly better make on the opterons, and the silicon used in opterons is better than the silicon used in x2's. the performance difference isn't that noticeable though, they both perform great. the opterons are known to overclock slightly better without complications, so if you are looking to overclock, opterons are some of the best.