There's a longish TTT in the Tour, though, so maybe from EF's point of view it would be better to have a team consisting of guys who can TT a bit better and to choose between Uran, Kangert, Van Garderen, Martinez, Craddock, Brown, Clarke and the classics guys and have Woods as someone who can actually achieve something during the Giro as Modolo doesn't appear to be a reliable guy in GTs and other big races. Or maybe they can send Martinez to have his first GT leadership. Not many options to choose from unless someone like Carthy has a breakthrough but he has always had poor recovery so it's a long way for him before he can do well in GTs.
If I were Woods, though, I would prefer to go to the Tour as well. When you're turning 33 this year, you don't know how many good years you have left and it would be a shame for such a good rider to never have the chance to ride the Tour.