I guess it's a matter of personal taste. I'm not an overly emotional person; in fact, I can be rational almost to a fault, and outbursts of emotion make me a bit uncomfortable. For that reason, I've always preferred characters who are more cool-headed and reserved. Sherlock Holmes has been a favorite fictional character of mine, for as long as I can remember. That's why I love Picard, too -- because he has an analytical mind.
Personally, though, I can't understand why you say Patrick Stewart "doesn't do emotion." He's one of the best Shakespearean actors I've ever seen. Have you seen him play Claudius in "Hamlet"? He was brilliant.