Interesting question. I'm going cull Schwarzenegger from this list, as I think both Depp and Stewart are better actors than he. So the question then comes down to the other two, and it's a fairly difficult one.
Johnny Depp is a talented actor capable of playing diverse roles. Just look at his recent portrayal of Murderous barber Sweeney Todd, even if it is a more macabre version of his Edward Scissorhands. Then compare that to his drunkenly swaggering Jack Sparrow. Even more, compare those to the wide eyed optimism of his Ed Wood. The man is versatile, I must say. Each of the character's are also played with depth, you can see the character standing as themselves, rather than as Johnny Depp playing said character. At least for the most part, I do make exceptions to his Willy Wonka(though in Depp's defense, after Gene Wilder it would be impossible for anyone else to fully take on Wonka as their own), and the aforementioned Todd. With a pretty eclectic background, and ability to fully absorb a character, I think he's a damn fine choice. That and I've always been a fan of the film, Platoon. And who can forget his bloody demise in his first film role?
Patrick Stewart is actually rather similar to Depp. An eclectic actor, from his over two decades as a member of the Royal Shakespeare Company, to somehow playing a space faring Frenchman, to his comedy role in American Dad. He has a resonating voice, an iconic look present in practically any showing he's in, and to a point, I may actually fault him for that. Which is hardly his fault, I know, but in the end it tends to leave his characters as "Patrick Steward playing blank".
And this is where I'm about to slip around actually giving an answer. On the stage, I'll have to give it to Stewart, the man is at home best in the theatre. On film, I give it to Depp, who, at least early in his career, was a chameleon. He was good, and you didn't immediately say that simply by virtue of him being him. If that makes any sense to any of you.