R-44 is faster and simpler. A taper who never used it before could make it go immediately, and figure out settings pretty quickly. Gain setting is simpler with individual physical knobs.
DR-680 is not difficult and is simple once learned, with more recording control options, but is a bit more complicated control-wise and card file system-wise. It has more physical switches on it to be concerned with. Gain setting can be linked to adjust multiple channels simultaneously in sync with each other.
If playback from the machine matters-
R-44 has individual channel out gains and EQ or compressors available, individual outs or 2 buss out, but 2 buss is always 1,3>L / 2,4>R hard panned.
DR-680 has a 2 buss mixer with individual channel gains & pans or individual channel outs, but no EQ, and no individual channel out gains.
Both have adjustable M/S decoding.