A male lion would beat a male tiger; hard to say about females, and here's why.
There is a show on the Discovery Channel or something, I can't remember. The show did computer modeling of these sorts of animal fights (others: wolf vs. cougar, Bear v. wolves, etc.).
With the lion vs. tiger fight, the tiger has the physical advantage--it is on average, much larger than a male lion. However, that gap is more than mode up for by the fact that tigers are generally solitary and hunt by ambush. Male lions don't even do hunting--what they do is fight other males for dominance in the pride. That training would make all the difference.
With females, lionesses do not fight each other in the way that male lions do, and they may not (in a fight with tigresses) have much or any "training" advantage.