Thor is an excellent rider and would make a quality addition to any team.
I don't think however that BMC can give him better support than Garmin. In the Tour, BMC will be much more focused on their GC ambitions than Garmin were. Thor could be their main sprinter, but really, he seems too smart to believe that winning mass sprints on flat finishes is a likely path to stage wins. There's no way that they would even consider having the whole team ride to protect a Yellow jersey for Thor for a week. That's something for teams with no ambition to actually win Yellow. In the cobbled classics, Thor will be the leader of a strong team, but he was also leader of a strong team this year.
This is without even considering the effects of Gilbert signing, and the potential conflicts of interest between him and Hushovd. Unless BMC are completely nuts, Thor would be a distant third on their list of priorities after Evans and Gilbert.
You would have to assume that the main motivation is money. That's not a criticism by the way, riders have short careers and Thor is getting on a bit. Making sure you retire wealthy is perfectly reasonable. But I really hope we don't hear him complain about a lack of support from his new team.