EDIT: Apologies: Didn't notice age of the thread. Please forgive.
Don't decide by us alone... check any firearm up close and in person, SAFELY.
I have neither seen nor handled a 783. Some on the interwebs would claim its a derivative of the 770, others would argue that it was something different than the 770. They would compare it more with the 700. (I would say insinuating that it was a derivative of the 700, not the 770.) I've also read the 783 has a 7.5 lb trigger pull (other sources say 3.5 lb). I do hope for the sake of Remington that it isn't the garbage their R51 pistol has turned out to be (New - in box: even factory reps can't reassemble it properly, so bad is the design), but more in line with the reputation of the 700.
I have had a 770 in my hands in a pawn shop and examined it and its action. The optics seemed okay. The general feel seemed okay. The bolt on the other hand, well... It was used mind you, but the way the bolt moved was quite short of smooth as it seem to catch and bind as you moved it in and out of battery. Maybe it was the way this particular one was treated, I'm not sure. However, the general consensus on the interwebs is the 770 is overall garbage. My short term handling of a single used one would make me tend to agree. But take what I say for what it is, an experience with a single used rifle.
To be honest I wound up getting a Savage Axis II. (It has an AccuTrigger, AND a Weaver Kaspa 3-9x40 scope right out of the box.) It didn't feel like worn-out junk when I got it new, and it still doesn't feel like garbage now.