It's been so long since I've seen the first movies, I can't really compare them to Mad Max: Fury Road (2015). I don't remember Max being quite so mad, though.
He's played by Tom Hardy (Inception, author of Wessex novels) here, not Mel Gibson. He's almost catatonic at the start, captured and tortured by the Immortan Joe, a messianic warlord, ruling an oasis with an army of radiation-poisoned war-boys. When one of his trusted lieutenants, Imperator Furiosa (Charlize Theron), takes off with his pregnant wives in a war-rig, he sends an army of modified muscle cars after her - one of them is driven by war-boy Nicholas Hoult (Hank McCoy in Days of Future Past). He props Max up on the front of his car like a living hood ornament and runs a transfusion line from him into his own bloodstream, stealing his vitality. Yes, in this dystopian future, everything is running out, gasoline, water, healthy blood.
This sets up the series of long chases and running fights that make up Fury Road. Mutants and uglies in chopped-up struggle-buggies chasing Furiosa and/or Max. It is brilliantly conceived and beautifully imaginative - although you might feel like you're seeing a video game with next generation imaging technology.
Although Max is pretty mad, Furiosa is just plain bad. She has a shaved head, dipped in black motor oil. She is missing an arm. She may or may not be able to kick Max's ass, but she certainly made a good attempt. And she never becomes a romantic interest or princess in peril. A lot of the time, this is really her movie.
So, mind-boggling, non-stop action, amazing world-building, great characters - and just enough depth behind the action. Takes the franchise to a new level.