I believe that a tiger would prevail over a lion. There are at least 2 reasons that lead me into the conclusion:
1) Tigers are, except South-East Asian subspecies (i. e. Indochinese tiger, South China tiger, Malayan tiger and insular subspecies Sumatran tiger, Balinese tiger - extinct, Javan tiger - also extinct) larger than lions (an important fact is that the subspecies of lion are less variable in size than those of tiger).
2) In the areas shared by both species (Persia, India) the tiger has been superior to the lion and expansive at the expense thereof (however, this fact can hardly be confirmed nowadays, since in Persia both species are practically extinct and Indian lions face extinction too - there are only about 150 individuals remaining in Gir Forest National Park in India).