In comments, Ivan G. Shreve and "Slowjack" make a good case that I've been unfair to the remake of The Man Who Knew Too Much. Certainly it's not a bad remake, and it's easy to see why Hitchcock preferred it: the remake has better lead actors overall, is more technically assured, and most importantly, has a real emotional punch that the original version did not have. Most of Hitchcock's British thrillers, even the serious ones like Sabotage, are kind of lightweight and emotionally cool. His American thrillers tend to be more intense, more emotional, more passionate; I think part of the reason critics used to prefer Hitch's British work (and while Hitchcock was alive, it was quite common for critics to say he went downhill after he left England) is that the earlier work didn't pretend to be anything more than a thriller, whereas his '50s films seem to aspire to more, and critics at the time weren't comfortable with the idea that a thriller could have things to say.
My problem with the remake is that while it embodies some of the virtues of Hitchcock's later work, it also embodies some of the flaws: it's very long and kind of slow (more than half again as long as the original), has a lot of bad rear projection, and doesn't have very impressive acting apart from the leads. (Alfred "actors are cattle" Hitchcock was not a great director of actors; good actors could give of their best for him -- as Jimmy Stewart and Doris Day do in this movie -- but supporting actors often did indifferent work in his movies because they're not really being given characters to play, just plot functions.) And while I appreciate the attempt to bring some emotional weight to what is after all a rather dark story -- it's about a couple whose child is kidnapped, after all -- it sometimes feels like Hitchcock and writer John Michael Hayes don't know whether they want to do a dark dramatic thriller or a somewhat lighter story.
Still, there's a good case to be made for the remake, and I think Hitchcock was accurate when he said that the difference between the two versions is that "the first was made by a talented amateur and the second was made by a professional." And there are few Hitchcock scenes more affecting than the final scene, where Day saves the, er, day by singing loudly so her son (being held captive upstairs) can hear her.