A friend of mine has a Rincon that I've been slowly but surely rebuilding for several months. I'm really close to finishing it now.
My .02.
They hold their resale VERY well. Around here a 680 Rincon in good shape will not go cheaper than $4k. The 650's don't bring less than $3500 unless they are parts bikes. These are not "like new" prices. These are used but still decent shape prices.
The gearing sucks, BUT the power makes up for it. My buddy's 680 will go everywhere any of the rest of us can go. I put a Big Red Gear Reduction in his but we haven't run it yet to try it out.
The ride is great. I like solid axles. For my uses, SRA makes more sense than IRS. That said, the Rincons ride like a Cadillac.
They are TOUGH as hell. I've worried and worried about the one in my yard. I knew that once my buddy trashed it I'd be rebuilding it. He's put it under three different times that I've been with him, and I think at least once more when I wasn't with him. It just started smoking last summer. Still ran like a top, just smoked. The automatic transmission that I thought would be toast if it ever went under was still fine. Not at all like the Hondamatics.
The guy that owns this one doesn't take care of anything. He runs it till it breaks, then buys new or gets me to fix it. He could break an anvil. His Rincon has about 5K on it and it has been abused to no end. Now is the first time it's ever had to have any work other than brake pads, a fuel filter, wheel bearings and oil changes.
I pulled the motor, put new oil pump chain and timing chain, new oil pump seals, Big Red Gear Reduction, .25 over piston and had the cylinder bored.
I also added a Foreman pod light some time ago. Not having a top light around here sucks when mud covers the lower lights.
For trail riding any really any use other than towing/work, they are great. New around here are pushing $10K out the door, and the design hasn't changed at all since 2006, so that's why resale is so high on them.
Even if you trash one people will pay big bigs for the parts. People cut the rear of the frame out with the IRS and splice it onto a Foreman frame to make an IRS Foreman.
The 650's had nikasil cylinders so they can't be bored. The 680's only have one oversize which is .25. If you ruin a .25 you have to go big bore or buy a new cylinder.
Like Mac said, 650's have drums up front, 680's have discs. You can put 680 discs on a 650 if you find a 650 that's a good deal.
From what I've seen the 650's can be tuned to put out more power than a 680. I haven't dug into any of them that far, but that's anecdotal "my old 650 was faster" from my buddy, and also from the Rincon gurus on Will Kostial's FB Rincon page.
My buddy's rear disc made noise. I put new pads on it and found the caliper was seized. Replaced both pads and calipers and it's been fine since. If you have an early rear disc go bad use the updated part and you won't have the problem again.
Fishfiles, my guess is sitting had ruined the fuel pump. They are just like the 420 fuel pumps and can go bad if you let them sit with ethanol gas in them.
If you can get it cheap (like $5K and under with those miles) I'd get it.