I don't get the hate for Broly (he has no personality, so I have no reaction to him) and I don't get the love for Bardock, though I do still "like" his character.
The big problem with Broly is his fanbase. if he'd just been in one movie and was sort of remembered fondly, that'd be one thing. But instead he was in three movies and is constantly hyped and requested as if he were the bestest villain ever…. despite being a literal giant baby whose entire motivation is he was upset by Goku crying. (And his design is kind of really awful.)
He's cool the first time around with the sheer bone crunching display he puts on and some of his lines, and at the time the true legendary super saiyan was surely a big deal. But for him to STILL be considered "the bestest ever" is just obnoxious.
As for Bardock, it's not about the special. Its about that last ten minutes where all his friends are kileld and he goes to avenge them, tears through Frieza's goons and faces him down even though he has no chance and dies instantly. Its a REALLY GOOD couple of minutes that makes up for any shortcomings the rest of his special has.
On my rewatch, the first Bardock special was painfully slow and you kind of have to wad through it to get to the kind of interesting character work, which is tragedy stuff that is done much better in many other series.
Bad guy with kind of human motives is something I love and not done badly here at all, though. So I like Bardock.