As above, Jackie Chan’s foundation is Peking Opera School…basically glorified gymnastics. Although a core component of that training is Wu Shu kung fu which includes the various animal forms and tai chi chuan etc.
Bruce Lee’s foundation is Wing Chun, which is a close quarters Southern Chinese kung fu style favouring linear movements and direct effective attacks. Wing Chun isn’t supposed to look good (like Jackie Chan’s kung fu), but is supposed to be effective. Although fans of MMA believe that wing chun is something to be laughed at – in my view this is because there are many practitioners who have little or no real skill. He didn’t complete the style so would not have ‘mastered’ the more advanced forms from wing chun. He didn’t think that flowery attacks were effective, but recognised they looked good on the screen so he learnt them. He then developed his own ‘style’ Jeet Kune Do which was effectively a style without a style. Basically you adopt what works for you. This is his contribution to martial arts – in my opinion, although a Hong Kong movie star, all he really wanted to do was master martial arts.
Jet Li competed in martial arts events after learning wu shu from a young age – he has apparently mastered various traditional forms (such as five animals and other Northern and Southern styles).
Someone mentions Tony Jaa…the style he portrays in his films and the video above is Muay Boran the original militaristic, non-competitive style that spawned Muay Thai. However, from what I understand he didn’t study this style, and went to an acrobatics school. He learnt tai kwon do…of which the Olympic style is largely ineffective against other more ‘martial’ based styles. There are many, many Muay Thai fighters across the world against whom, Tony Jaa would lose a competitive fight.
This is all my opinion of course. Calling a martial art ineffective is a sensitive topic as you’ll offend any practitioner of that style. It largely depends on the individual…you could argue that all of those people mentioned are movie stars first and martial artists second.