I prefer 1964 to project64, its faster and I believe it is slightly more compatible with some games, it can run Banjo-Kazooie/Tooie better as well as Donkey kong 64(which still doesn't work right but at least polygons aren't flying around). the GUI is better as well.
1964 0.8.5 is best for Banjo-Tooie, who says old versions are worse?
However! Project64 is the choice emulator for Conkers bad fur day for sure, as well as the fact Project64 is out of the box working usually, 1964 requires more setting up.
Simply put, both emulators have their merits, both are nearly exactly the same in compatibility level, one is faster than the other.