Your total accumulated Tourism vs. the total accumulated Culture of each civ is what counts. Difficulty level matters a lot as far as the numbers are concerned, and the opposing civs to a lesser degree, but generally the longer the game goes on, the harder it becomes to overtake the top Culture-producing AI's. A general approach is to get any possible theming bonuses you can, get as much Culture that will translate to Tourism(*) as you can, finish Aesthetics, tech to Refrigeration as fast as possible for Hotels, Radar for Airports, Telecommunications for National Visitor Center, and The Internet for The Internet. If all else fails, use Great Musicians to perform Concert Tours in the highest Culture opponents.
(*)Culture that will translate to Tourism
Great Works
World Wonders
Natural Wonders
Improvements(Landmarks, Moai(Polynesia), Chateau(France), and, although the Civilopedia doesn't say, I think the Brazilwood Camp(Brazil) works too)
I recently won a game on Prince(Standard size, Standard speed, France, Pangaea) on Turn 266 only making it just past hotels. Tourism per turn was +123. Two cities, no war, no World Religion, no Louvre theme, no(or very few, 2 at most) Archaeologists. Mostly through World Wonders, theming(France + Aesthetics finisher = AWESOME!) and a few chateaus plus hotels.