I haven't really had a need to use these types of programs in quite some time now, but when I did use them Azureus was my choice.
It seemed more user-friendly to me and was easier to use and understand.
I have tried Limewire, but that thing seems diseased with people who just want problems for other people. Almost everytime I've used it, the file I was downloading had something wrong with it. It was usually a virus, a trojan, corrupted files, empty files, etc.
There is an unusually high proportion of people on Limewire who do this sort of thing than on any other programs I've seen or used.