In a recent interview Dak was asked how he has improved his accuracy. He said that he's concentrating on his footwork and feeling more comfortable with the offense. It's working. He's accurate more consistently now than he was back in college.
His pass protection has been quite good. That's a big factor in his success.
Having a smart center in Fredrick helps.
As others have mentioned, defenses have been stacked against the run and Linehan has done a good job of playing to Prescott's strengths (e.g., ability to throw on the run),
Highly experienced and competent QBs such as Romo impact games with their pre-snap reads and adjustments. As an inexperienced pro QB, Dak can't do that to the same extent. But I do think that coaching in general has gotten much better over the years, in college and in the pros. The rookie QBs are more sophisticated than they used to be in part because college schemes have become more complex and college coaching has improved.
It could be that the main problem with the Stoerners, Hutchinsons, Leafs, Carters, Wrights, etc. had more to do with the limitations of the players (and not the coaches). I guess it is possible that Steven McGee could have been a Pro Bowler with the right coaching, but maybe he just didn't have what it took.
It may be difficult to wrap one's head around it, but the Cowboys coaching staff must be doing something right with Prescott.
A couple of other things -
Prescott's supporting cast was much better in 2014 than it was in 2015, so it isn't surprising that Prescott looked better in 2014 (particularly before he got hurt running the ball in 2014). Some of the draftniks who weighed in on Prescott's pro potential focused on his 2015 and underestimated him.
The ill-timed DUI arrest before the draft was a red herring, but understandably didn't help his draft status any.