Hopper, Per Sera on SGW some differences are
"682: Has adjustable trigger placement....maybe 3/4th inch ; has replaceable shoulders (never saw one replaced??) and are usually heavier by 1/2 lb.
686 : less engraving , lesser wood neither of the two features above"
I should probably have shot a 686 yesterday, but I am concerned that too light a gun might beat me up over time. As for adjustable triggers, I don't know how important that is. They adjusted the trigger all the way back for me on the CG I tried and the LOP was still nearly a half inch longer than what I am used to on the 870 (which is not to say that the 870 LOP is what I really should shoot). I am not what sure what the idea is behind the adjustable trigger. It may save cutting some wood or adding a spacer if the LOP is slightly too long or short, but I wonder if it is nice to have if you are from a region with weather in which you shoot in a polo shirt in Summer and a heavy jacket, if at all, in winter.
As for the eye candy, it is nice and I would love to have it but can live (I think) with a simple gun.
Edit: I am not to sure about the SP1 being light. It isn't readily findable, at least for me at the Beretta site. I heard they are light, but one dealer lists the SP1 at 7lb 10 oz and the SP1 Field at 7 lb 4 0z. Both are 12 ga and I beleive both are 30" barrels.