I love this trade. Having watched a TON of Capitals hockey over the last 5 years I'll give you my take. Basically...
I don't agree with your assessment of Vrana. In the last two years he's scored 36 goals in 108 games. Good for 3rd on the Capitals behind Ovechkin and Oshie. 35 of those goals came at even strength. He also did this despite significantly lower even strength ice time than most of Washington's regular forwards. During those same two years he had 15 powerplay assists despite being on Washington's 2nd powerplay unit. If you watch the Capitals you'll realize that they rarely give time to their 2nd unit, and if they do it's not much.
The reality is that Mantha relies more heavily on the powerplay for his production than Vrana does. Vrana is a much better even strength goal scorer and he's about to see a sizeable increase in ice time with a top center (his best center previously was Lars Eller). Plus now that he's on a top powerplay unit he's likely to see a significant increase in PP ice time, which is good for Detroit (and Vrana's stat line) because he's a great powerplay passer and the first legit playmaker we've had off the half wall since Datsyuk and Zetterberg.
Vrana's warts are these: He's not super defensively responsible, and he's not super physical. It's legitimate to wonder how he'll handle better competition that comes with increased icetime, but with that said he's not Andreas Athanasiou either. He's more competitive and responsible than THAT. FWIW he's also been one of Washington's better possession forwards over the last two years.
I think we actually got the better player here, he just needed to not be buried down lineup. Especially when you consider Mantha is likely to take a hit in icetime. This will hurt especially bad on the powerplay because his usual spot is occupied by a playmaker in Washington's system (typically Backstrom or Kuznetsov). He'll be the shooter on the second powerplay, and as I've already mentioned that unit doesn't get the same icetime that Mantha was getting in Detroit.
Edit: Final thought. I'm pumped about the 1st too. I think Washington is getting bounced early. Nobody on that team gives a sh*t anymore and it's evident. They won their Cup and now they're content to go as far as their talent takes them without doing the hard work. They're primed to get beat by some hardworking up and coming team. I don't see them making past the 2nd round and maybe they get bounced in the first depending on their matchup.