In my humble opinion I find the Tony-Scott-hem! of Man on Fire and the Bayhem! of Bad Boys II quite similar when it comes to cinematic language. Both are designed to induce a strong level of Adrenalin through intense imagery and sharp editing. Tony Scott is taking his movie obviously way more seriously. For Michael Bay it was just a therapy session after he needed to, at least try to, take Pearl Harbor seriously. Which was his previous film. So Bad Boys II is extremely flamboyant.
Both directors utilize a great amount of long lens ( 75 mm ) hand held footage. Both directors cranked up the contrast of the film to extreme values. Bay did seem to use more saturation and color variations thought. While Tony limited the color scheme to a few earthy tones and ugly greens.
Tony uses overlaying footage one over another to create the effect, which will set people on edge. Michael uses more dynamicism for the same effect. He will find just the right shots and just the right moments in those shots to assemble a suggestion of a moment
Sergei Eisenstein style. While Tony would overlay them and supermessify them, Tony Scott style. Also Michael Bay's shots appear to be cleaner. And Michael is using a short ( wide ) lens more frequently, which lets him make way more pretty pictures way more frequently. For a movie like Bad Boys II which is designed to be a fun pop-corn ride, this is a correct way to go. While what Tony does isn't a fun pop-corn ride, but a brutal tale of revenge, with a twist.
If you look at something a bit more serious from Bay, like say 13 hours, where he takes a serious situation very seriously. You can see he seizes his beauty shots, instead shooting most of the serious tension stuff with a free hand held camera. Which is not quite the same technique as what Tony Scott does with Man on Fire. Michael Bay never overlays footage over itself from different takes to create disorientation. But it feels already much closer, since Tony does shake the camera quite a bit during the tense stuff. And relaxes the camera during the not so tense stuff. Kind of like what Michael Bay does as well.