Here's how one of my fav authors, George RR Martin, answers that question [in reference to his Song of Ice and Fire series]:
"I don't concern myself over whether my characters are "likable" or "sympathetic." (I had my fill of that in television). My interest is in trying to make them real and human. If I can create a fully-fleshed three-dimensional character, some of my readers will like him/ her, or some won't, and that's fine with me. That's the way real people react to real people in the real world, after all. Look at the range of opinions we get on politicans and movie stars. If EVERYONE likes a certain character, or hates him, that probably means he's made of cardboard. So I will let my readers decide who they like, admire, hate, pity, sympathize with, etc. The fact that characters like Sansa, Catelyn, Jaime, and Theon provoke such a wide range of reactions suggests to me that I have achieved my goal in making them human."
Do you agree? I think a sympathetic character can be drawn that will be likable for the
vast majority of the readers and still not come across as cardboard. However, don't be afraid to give your protagonist flaws and your antagonist positive traits. Martin takes this one step farther, drawing many characters that are hard to peg--to great effect.