I'll play devils advocate with a couple other things to consider:
Price-
May or may not be a factor, but one simply cannot beat the cost of a new DR-680 for a 6 channel/preamp recorder.
Quality of the recordings-
The newer SDs and Zooms being discussed are great recorders you will be able to make great recordings with. Will those recordings be better than those made using your DR-680?.. maybe but probably not significantly so.
Ease of use-
All of the newer recorders are more dependent on menu use, so consider your personal tolerance for that and how it relates to how you will work. DR-680 is super easy to use and reconfigure, the others typically take more time to setup the way you want, and are more likely to have unnoticed settings "doing things". The others generally provide more options for power users at the cost of more interface complexity.
Functionality-
DR-680 has digital in/out, and can gang all channel gain controls together for simultaneous adjustment with a single knob while retaining individual channel gain offsets, meaning ganged channels don't all have to have the same gain <F8 can gang but all ganged channels must have the same gains. Not sure about SD.
I went from 680 to F8, driven primarily by the need for 8 channels with preamps. I power it using the same Tallentcell battery I picked up near the end of the time I was running the 680 regularly, which provides simultaneous 12V, 9V and USB (5V) outputs and lasts a full day or more of recording. I sometimes miss the digital in/out (rarely), the ability to gang channels while retaining individual gain offsets (often), and the lack of individual channel outputs (often for me but probably won't matter to anyone else). Other than those things, I love the F8.