Morneau is, at this point in his career, a platoon bat (.569 OPS last year vs. LHP). We already have that guy, he's Adam Lind and he sucks. I'd rather have Willingham's superior bat and lower price tag.
I'm at work and far too lazy to look up the numbers, but Morneau's numbers (in general, but especially) against LHP were ghastly at the beginning of the year, but were much, much better down the stretch. I'm guessing he'll be closer to that later part of the season than the beginning or even the aggregate.
Honestly, I don't know. Morneau's definitely overpaid at $14 million this year. But I'd hate to see the Twins sell low on him this offseason after nursing him back to relative health over the last two and a half years, only to have him break out for someone else. If they're going to trade him, I'd say do it at the deadline. Someone will need a bat, and someone will pay handsomely for him then. Same with Willingham, honestly. That also gives time to find out if Chrissy Chrissy Parm Parm and Hicks/Arcia will be ready to play next year before trading decent players.