there are only a handful of games that mupen64 emulates better than pj64, and some of these are already resolved through the changes in the 1.6.1 plugins jabo released recently.
There are also a handful of titles that mupen64 has issues with as it does not include memory patches in the rom settings file
Pokemon snap no input response in the first mission
Zelda64's subscreen taking forever to appear after pressing start
Zelda64's equip screen, link is low resolution (Rice video does not enhance the internal resolution of the copied framebuffer, and the defaults do not even enable the framebuffer compatibility settings iirc)
Of the front ends i tried for mupen, one of them does not even save applied settings, and the other does not respond to input after starting a game (while it responded in the input config screen......)
Accurate is highly subjective, the only "Accurate" n64 simulator is MAME, the rest are all mostly HLE based with an LLE Interpreter tacked on as a second thought.