Honestly, I think modern MMA has helped to unpack this question a bit. After all, we've seen strikers with no grappling game get humiliated by grapplers back in the early Gracie days, and we've seen grapplers with no striking game get utterly devastated by strikers (see how much of the Yoshida/Crocop fight you can stomach).I think a lot depends on how much one person can make the other play into their strengths, and how well they know what to expect from their opponent. A grappler who knows how to defend punches has a much better chance than one who blocks with his face. The same can be said for a striker who knows how to sprawl out of takedowns, or defend basic submissions.
That's great, really puts the issue into perspective. Makes me remember the first time my Kung Fu sifu let me spar with a visitor who had wrestling experience (as opposed to an experienced student). I made a *lot* of contact with elbows, fists, knees, and feet before he took me down, and of course I knew nothing about being on the ground. I had never even heard the term "ground work" and I didn't know how to maneuver.I still remember getting up and bowing awkwardly after being pinned and seeing a big grin on sifu's face. He said, "you know, if you had lifted your leg up like this a little bit he couldn't have done a thing." He showed me what he meant and I discovered there was a new dimension to this stuff.I realized that yes, sifu knew how to maneuver on the ground, and no, he wasn't going to be teaching it to me anytime soon, but someday I would be able to learn it and *add* it to what I already knew.That's what a lot of the critics forget - even if you study a martial art where you only use two fingers on one hand, better get good at it and you won't regret the effort put in.Now that I'm in Judo I'm *very* glad for the years I spent doing kung fu. When I share with newcomers that I used to do kung fu, I get LOTS of sarcastic comments, assuming that I've learned my lesson now and that I'll never go back. All of them are of course based on repeated viewings of more modern versions of the video you just posted.