Ultimately, I think this is the reason Stark wanted Logan on the team in the first place. He's simply more willing to kill if necessary. And for at least a potential global threat, there's a chance that Logans way might actually be needed. Emphasis on the word MIGHT.
Sometimes... not always but SOMETIMES you can argue you need a killer. 99% of the time I do think Caps way is better... it's that 1% where a Logan can make all the difference in the world.