The guy on the Les Paul type is playing mainly open chords, with a thumb on the 6th string in places
The guy on the Strat seems to be playing "power chords" or "5ths" - which are often just 2 strings to get that "chunky" sound - e.g. 3rd fret of low E string (G) and 5th fret of the A string (D) = G5
He is then resting his hand over the rest of the strings to mute them and get that percussive "chunking" sound to compliment and contrast with the open chords of the other guitar
The Strat guy looks like he is playing a sharpened 5th to give an "augmented" feel in places (I can't hear properly at work to verify)
This can sound great on dirty guitars to give a sense of movement by sharpening the 5th but keeping the root note where it is - makes a great passing chord either up (by sharpening the 5th) or down (by flattening the lowest note - which is the same as sharpening the 5th of the lower "chord")