Easy pick for me - Die Hard
I was familiar with Mel Gibson and his work prior to Lethal Weapon, I thought I'd got a grip on him with Mad Max, silent, expressive eyes, a look that could pierce armour and then LH came out, loud, big hair, extrovert but dark, this was Max but having not taken his medication for a week.
LH allowed the 80's films that had gone before to settle and then add the jokes that actually were jokes not merely a seg-way play on any particular violence that presided that said event. My god, there was even a plot. Gibson & Glover work wonders together, no doubt, but for me, I couldn't then and I certainly couldn't now (if I tried) get into these films as if I loved them, not like I can the winner of this QF for me, Die Hard.
Die Hard was the Spaghetti Western of the action era, the lone man, against a tower block full of yuppies at Christmas, no wonder he went on the rampage !
I find both Gibson and Willis hard to like, as people, as actors, both relentlessly smug and un-self aware, it's like a cloud of ******** has drifted over them and stayed with them, but Willis' character here needs that, to see him through, the wise-cracking gumshoe with no hope, no money, and no chance fire-cracking his way through the many to get to a villain so whip-smart, he comes with health insurance.
Die Hard gives the viewer everything you'd want in an action flick and more, action (plenty), jokes (lots) and a plot driven by the actions of the characters rather than being pulled along by circumstances of bombastic tenacity (see Arnie films).
It's not heralded by many as the 80's action flick for nothing, the setting, the odds and the script add a huge amount, but principally it works due to Rickman and Willis, and the tete a tate towards that ending.
Only one winner for me in these two pairings, bad luck Riggs, but I am too old for this s**t.