The lions and tigres live in a large (40 acre I think) safari and do short periods of ‘duty’ in these cages so that Zoo goers can see them without paying the price of the safari trip. You can see where they usually live in videos like this
Search results for videos of the Safari and Zoo
Official Videos of the “Akiyoshidai SafariLand” establishment
Tigers are generally more aggressive apparently. But the lion was not at all scared.
The Wikipedia article comes out (marginally?) in favour of the tiger https://en.wikipedia.org/wiki/Tiger_versus_lion I think that lions are natural born fighters, since they live in packs and fight to be top male in the pride. In such same species male on male bouts, such as rutting and dog fights, the fight usually ends when one is party is subdued since the objective is to establish superiority and mating rights not to kill the same species male.
Tigers on the other hand are solitary, not used to fights, but eating animals of other species, so may rather be natural born killers who may be more inclined to treat a lion opponent as prey. In the above video the tiger seems to be stalking the lion as it would prey, whereas the lion seems to be treating the potential fight as a sort of bout.
Thus as expressed in the wikipedia article on Lion’s versus tigers when tigers and lions meet in the wild, or in random situations, the tigers tend to win. However, importantly, in circuses where the big cats have been pent up and made more aggressive, the lions tend to kill the tigers. I.e. perhaps if Lions become nasty, and fight to kill rather than show superiority, then perhaps their defensive armour (their mane) and attacking fighting style may give them an advantage. While the expert opinion comes out in favour of the tiger in the wikipedia article, this Popular Mechanics article is pretty convincing to me. https://goo.gl/wxWgHn
The same lion trainer (killer) explains how the footage of the Big Cage here https://www.youtube.com/watch?v=YmYYpGzmop0 was made here in The Milwaukee journal July 18, 1962 http://images.yuku.com.s3.amazonaws.com/image/gif/f4826dc5d50606ed235b18234caf25ad70d5e4a2_r.jpg he claims that they needed to use three tigers since the lion killed the first two so quickly that they did not have enough footage.
If boxers were to meet someone that fights to kill, poking eyes and kicking testicles, the latter would win initially until the boxers realised that fight was to the death, the superior skills would prevail. But then, tigers are generally bigger, so I am not at all sure.