@talk72000,
Just admit you are one of those crazy tiger lovers.
Even if you are right that tigers can run faster than lions (and that's debatable), the hypothetical involves a fight, not a race.
And you're not sitting in an armchair? Does that mean your stage animal fights for a living?
Any sane hunter fears a big cat...including lions.
It may be that lions and tigers are equally matched, but the difference in natural habitats is most likely meaningless.
At first the West saw the male lion as this magnificent killing machine, and then after some study it was determined that they are the spoiled feline Pashas of harems of hardworking females. Further study has showed that they hunt more often than previously thought.
They always have been known as the protector of The Pride, whether it be against other male lions, leopards, or hyenas.
That is specialization, and for a specialized task -fighting- the specialist usually wins.
Now, if we are looking for the biggest bad-ass in nature, the award goes, hands down, to the wolverine.
99 times out of a 100, a tiger or lion will kill a wolverine in a fight, but more often that not, the wolverine will drive off either of the big cats.
In a beast on beast fight in a cage, where neither could run away, my money will be on a bear...Polar, or Grizz