I have several rem 700';s of all different ages (newest will be a 2014 SPS one in .243)
and forms, plus a bunch of custom built riffles on there actions!
all have been great rifles and shooters
I also last yr picked up a mossberg patriot , but in .223
my opinions on it are this, its a nice gun for the price, but it is just that a CHEAP gun
they have issue's on larger calibers with more recoil, causing stocks to crack, so if you get one, bed it, seems to solve that issue, and well, won't hurt it any on accuracy help
mine shoots OK, not tack driver, but will hold about a 1.5 inch group with most ammo I stuck down it to date, haven't really played with it much, was an impulse buy deal, and price was right, think I got it for like 320 bucks out the door, brand new!

the action is rather crude, not smooth like a 700 by any means, but it works?/
the rem 783's
haven't owned but shot a bunch, mostly in 30-06 caliber, some shot great small groups and some didn;'t
seems like pick of the litter on them there!
all three guns your looking at at OK deer rifles
the 700, pending what form(ADL, SPS< BDL< CDL< OR??)
will determine how much time was spent on fine turning them from appearance to how smooth the actions are, and what stocks and set ups will work, some of the cheaper lines , are NOT so adaptable for building off of, as the actions have slight differences that make it a little trickier to do so!

ALL can be made better too if wanted, same with most rifles today!
if you plan to keep the rifle forever and don't mind the added costs, buy the 700, in a better trim level
if not, its a coin toss maybe between the two cheaper lines IMO
the Mossberg wins the war on custom like looks?
both are cheaper made rifles however! don't expect the best of anything on them!