The differense between the Tiger and the Thunderbird sport hub is only cosmetic. I think the Sport one looks better, so that's what I have on my bike.
One reason for people saying it doesn't fit, is the difference in rimsize. The Thunderbird Sport has a 17" front rim which is 1" smaller than the Speedmaster. I shortened the fork and use a 19" rim. Makes it look so much better! Lowered it at the rear too. I was trying to upload some photos but I don't know how, I'm afraid. But you can see pictures in the latest issue of the "Spirit", Triumph's web-magazine.