Uber spears aside, I just always have better luck raising Hector than Eliwood. Lyn usually gets good level-ups in my files, too, which leaves poor Eliwood cold and alone, shivering on the sidelines. (Or maybe from the relative safety of Merlinus's tent.)
At any rate, Eliwood does have a personality; he's quiet, thoughtful, and a romantic.
But generally people prefer characters like Hector. I like Hector-- he's so rude and he doesn't even know it. But if I ever met someone like him in real life? I think I'd want to punch him really hard. I wouldn't actually do it, but...
Eliwood would be that rational, always-able-to-depend-on-no-matter-what kind of friends. You could trust him with a secret, get advice from him, et cetera, without any worries about him not taking things seriously when they needed to be. He does have a sense of humor, too, which is nice. (You have to have some sense of humor to hang out with Hector, of course.)
And Lyn's kind of a mix between Hector and Eliwood, IMHO. Mature, serious when she needs to be, playful when she knows it's okay to be, et cetera. She's got a sense of humor, and I think she's witty, too.
At any rate, best =/= favorite. While Hector has always been the best "lord" character, with all kinds of maxed stats, he is not my favorite. Lyndis is.