With Tennant, I rarely get there's much behind his acting. It's primarily on the surface: here he looks sad; here he looks angry and barks at people.
With Eccleston, there's the sense that his actions come from somewhere inside the character. You can see him processing thoughts, assessing the situation, leading to a response. Tennant's Doctor mostly just... does things, because they're written that way. Then to disguise the lack of genuine flavor he spices up his performance with all these affectations. Mannerisms. He's like a cartoon, or a well-trained monkey.
Sometimes it can be cute. Sometimes he drops all that, and it seems that we get something real. Most times, the yippiness annoys me.
Matt Smith, what little I've seen of him, his strangeness seems based more in a genuinely awkward and eccentric psychology, rather than "wacky" behaviorisms. He's grabbed me -- with his frustrated hands -- from first I saw him and heard him speak.