Vereen is far more versatile than your traditional 3DRB for two reasons:
1. He can run between the tackles. The Pats used him as the goal line back pretty frequently last year, and it wasn't just for versatility - he pounded it in there a few times. Not many 3DRBs can do that.
2. He isn't just a receiving threat coming out of the backfield. He can shift over to WR, credibly run deep routes, and make deep catches over the shoulder. How many 3DRBs can do this?:
Tom Brady passes deep to Shane Vereen for a touchdown - YouTube
I do want to specifically address this, though:
I think you're somewhat missing the point here. It isn't just that Vereen can be a downfield threat. It's that he has the versatility to run between the tackles and be a downfield threat. Which means that you can wait for the defense to declare how they're going to defend against him, and react accordingly. If they put a linebacker in there, you shift him out wide and let him run deep routes against defenders who have no business covering him. If they put a cornerback on him, you can hand the ball off to him knowing that you're facing a softer run defense.
In much the same way, if they put a linebacker on Gronk, the Pats will probably audible to a pass and throw to him. If they put a safety on Gronk, then you run behind him.
And that's where it gets really intriguing: defenses are going to have to account for both Gronk and Vereen, and no matter what they do, they're going to have critical matchup issues against one of them. You either come out in a formation that's critically underpowered against the run or one of those guys is being covered by someone who has no business covering him. This is before you even bring other matchup problems to the table, such as Amendola being virtually impossible to cover with one guy or Dobson/Boyce potentially commanding deep safety help.
Edelman, by comparison, is easy to defend in theory: you just stick a corner on him. He doesn't create mismatches. There will literally never be a scenario where he is covered by a linebacker, which is something that happens regularly with Vereen.