In the last two years, both of these guys have had career years with the bat.
2011 Mike Morse: .303/.360/.550; .241 ISO; 31 HR, 95 RBIs; 3.3 WAR
2012 Adam Laroche: .271/.343/.510; .238 ISO; 33 HRs, 100 RBIs; 3.8 WAR
For WAR, it should be noted that Fangraphs started weighting defensive positions in 2012.
So, essentially, Laroche's prowess with the bat was worth an additional .5 WAR. Morse, on the other hand, was significantly better offensively. However, one could make the arguement that a full year of Adam Laroche was a critical part of Ian Desmond posting positive defensive numbers for the first time in his career.
The question becomes, who is most likely to repeat, or hit closer, to their career year? Prior to 2011, Laroche was remarkably consistent in his career. He averaged .271/.340/.488. Good pop, decent OBP. Morse is much more difficult due to his history of injury. But since coming to Washington, he's posted a .296/.345/.516 line. That includes last season when he was still gettin back from injury. We saw Beast Mode really turn it on from the last week of August, slugging at .500 and hitting like the Beast Mode of old.
I don't put a whole lot of faith in the lefty/righty matchup. Good hitting is good hitting and will deal with lefty or righty. However, Laroche does noticeably poorer against LHP, where as Morse does not. Essentially, we would be playing Tyler Moore against left handed starters and possibly using him to pinch hit for Laroche against lefty specialists. Overall, when healthy, Mike Morse appears to be a better hitter than Adam Laroche.
Defensively, we know Laroche is a lot better. He's one of the best defenders at first base in baseball. Is his defense worth a whole lot at first? How much do you value him reducing throwing errors of other players?
Then we have to factor in age. Morse will be 31 next season. Laroche will be 33. A 3 year contract puts him at 36 years old. With Morse only having one year left we only care about his performance next season. All in all, I think Morse is more likely to hit to his Washington averages at 31 than Laroche will be through 36.
Overall, I think I prefer Morse. However, that is dependant on what MOrse could get in a trade.