Jimmy Stewart movies with Hitchcock: Rope, Rear Window, The Man Who Knew Too Much, Vertigo
***or***
Cary Grant movies with Hitchcock: Suspicion, Notorious, To Catch a Thief, North by Northwest

I think it's a tossup.

OK, here's the story: Stewart really wanted to do "Vertigo", and Hitchcock wanted Kim Novak as the female lead. To borrow her, Stewart's studio agreed to loan Stewart to Novak's studio for a follow-up pairing in a piece of fluff called "Bell, Book & Candle." But Stewart's contract contained an "out" clause: he could delay making this picture if he made the next Hitchcock film.

While shooting "Vertigo," Hitchcock began working with the star writer Ernest Lehman on the script for "North by Northwest." Stewart loved the script, and Hitch told him that he could have the lead role. As the project developed, though, Hitch found himself thinking of it more like "To Catch a Thief" ... but he didn't tell Stewart.

When "Vertigo" wrapped, Hitch told Stewart that he was having problems funding the film under his (Hitchcock's) production company. Stewart even tried to see if he could arrange funding ... but finally he had to report to "Bell, Book & Candle." The first week that "BB&C" was in production, Hitch made a deal to give the movie to MGM, which was holding Eva Marie Saint to co-star in it! And it just so happened Cary Grant was available, too. So Stewart had to make a movie he didn't want to make, while knowing Cary Grant was making the movie he did want to make...

One interesting thing -- for someone with a reputation for hating actors, a remarkable amount of dialogue in Hitchcock's films is improvised. Stewart, Grant, and Grace Kelly were permitted to improvise at will. An entire scene between Joseph Cotton and Teresa Wright in "Shadow of a Doubt" was dreamed up by the actors, sketched out by Thornton Wilder (who co-wrote the screenplay), and then improvised. Of course, there were some actors that Hitch did have to browbeat (Montgomery Clift comes to mind) -- but Hitch got great performances out of them as a result!