Back in college I witnessed the following conversation [topic=Remo Williams vs Samurai Cat]:
Friend#1: “Remo Williams would . . . [lengthy description about how he can never be hit, he never misses, and he always kills].”
Friend#2: “Yeah, but Samurai Cat would . . . [lengthy description about how he can never be hit, he never misses, and he always kills].”
Friend#1: “Yeah, but Remo Williams is the avatar of Shiva the Destroyer.”
Friend#2: “Yeah, but Samurai Cat is a stud.”
"In Satyam, Shivam, Sundaram or Truth, Goodness and Beauty, Shiva also represents the most essential goodness.
Shiva is the god of the yogis, self-controlled and celibate, "
I’d say it’d be an even match, with Doc disadvantaged by his reluctance to kill.
Of course, as an all-around hero, Doc has about a hundred other high-level skills that Remo probably doesn’t. In almost any kind of tight spot, I’d prefer to have Doc on my side.
I’m a little surprised that Remo appears to be the overwhelming favorite. Both guys are pretty much physical perfection…but Doc is bigger, probably stronger, and definitely smarter. Remo is more lethal, and may be faster. In a MMA style fight, it may well go the time limit with neither man able to land a decisive blow…
But Remo doesn’t fight. Remo kills. Doc’s dust.
There’s always the possibility that Remo will pause and ask, “What the Hell’s that trilling sound?” and wake up in Doc’s Mental Hospital for Bad Guys. 
Remo is capable of shoving his hands ythrough, well, anything. I don’t recall the Doc being able to do that. It’s not a matter of martial arts. Remo Williams is basically magic.
The only explanation I have for Remo no being the unanimous favorite would be that those who disagree aren’t familiar with his abilities.
The truest statement above is that Doc is smarter than Remo. But then, your average toaster may have the edge on Remo in that department. That Remo is challenged as far as technology goes is truly the understatement of the century.
I don’re recall ever seeing solid numbers as far as Doc goes, but hearing that he could dead lift a ton wouldn’t surprise me. Remo could juggle a ton.
Remo has simply been trained and formed into something that is beyond human.
Doc probably has a gadget that will tell him how many people are in a house before he goes in. Remo just listens and counts their beating hearts.
Doc has light body armor that shrugs off machine gun fire. Remo can see the incoming rounds and step between them.
Doc has night vision goggles, possibly glasses, or maybe even contacts by this time. Remo has that ability with his naked eye. Or, if he is somewhere, say underground, where there is absolutely no light at all, his other senses fill in and he knows exactly his surroundings as well as if he were standing in a sunny field.
Some people have a sixth sense whereas they can tell if someone is looking at them. Remo knows if he’s the focus of someone’s attention a mile away, say, through a sniper scope. Or a telephoto camera lens.
Doc would be disadvantaged by his prohibition on killing. So we make the ROE non-lethal. Remo can literally move faster than the eye can percieve. Doc would be paralyzed or unconscious before the sound of the opening bell died out.
Remo, without a doubt. Hey, he’s the Master of Sinanju. After Chiun, of course.
You’ve said exactly my thoughts on the subject.
It’s ‘Chiun’ according to the IMDB, and he doesn’t walk on water.
“You must run … very fast.”
Oh yeah, and
“You move like a pregnant baboon!”
