i also like dawn but not connor, so ill try to decipher why thats the case.
well, as some people have kind of said, dawn is a bit more relatable. when she whines, it can be about typical teenage issues that anyone who's been (or is) a teenager could understand. of course, some people might still get annoyed, because understanding why someone is screaming and whining doesnt make it less annoying. still, connor, in comparison, grew up in a hell dimension and has all this complicated stuff going on, which id be surprised if anyone said (honestly) that theyd been through.
as for dawn acting her age, it makes sense to me. based on the impression i got from 'real me', with buffy not wanting to show her the dead guy, joyce not wanting her involved in a murder scene, etc. it does seem like she was sheltered more than the other scoobies from the demon world. plus, there's the whole "they wanted dawn to be a younger age, but made her a little older because they wanted michelle trachtenberg" schtick, but thats part truth part fanwank. anyway, i believe that for her age, dawn wasnt particularly immature. teenhood is a crazy time, and i know a couple of teens that act that immature in real life. still, though, those teens can be just as annoying as some people find dawn. oh well. i guess thats why some people only like her season 7 and on.
theres also the fact that dawn's annoying-ness came from all her screaming and crying, whereas connor's was crueler (such as trying to kill his dad), due to his different issues. maybe whiny, screaming teenager is less annoying than cruel, homicidal teenager? hey, i can only speculate what everyone is thinking. ...well that and read these posts 😀. all i know is that i like dawn in all the seasons she was in, but i dont really like connor.