Both, actually. S1 Gwen's characterisation is no more shaky than everyone else's (except for Owen, who is the only consistently written character in s1), but she's the pov character at the start through which we get to know Torchwood, which makes it more noticable. (I myself was indifferent to Gwen in s1, but then I was indifferent to everyone, including Jack, in terms of liking, but thought Owen was interesting. (Not the same thing as liking.) I'm not sure I would have continued with the watching if it hadn't been a DW spin-off.) It was in s2 that I got to love them all.
HOWEVER, I think most of the hostility towards Gwen is due to the Jack/Ianto, and the irony here is that she doesn't interfere with it. Gwen and Ianto are friends. Ianto and Jack are having sex throughout the show. (This is actually a Ianto characterisation problem in s1 where you're supposed to believe he goes from "I hate you and want to kill you, Jack Harkness!" in one episode to "sex, Sir, pretty please?" in the next but one without blinking. There is some clarification as to why that happened in later s2, but at the s1 time it made it impossible for me to take Ianto serious as a character) There is some UST between Gwen and Jack, but not only is that the case between Jack and everyone, but when push comes to shove in the first third in s2 and she has to choose between Rhys and Jack (and in a very important matter - this is when Rhys finally finds out about her secret job for good, and Jack orders her to retcon him, i.e. wipe his memories), she chooses Rhys. However, I'd say through the show it's clear Jack doesn't see himself in a monagamous, OTP-like relationship with Ianto (there is a time-travel episode in s1 where Jack falls for another man, and when asked whether he's in a relationship back home, he clearly says "no, there is no one"), and fandom being fandom, this is clearly Gwen's fault. Despite her not having an affair with Jack, or doing anything to interfere with Jack/Ianto.
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HOWEVER, I think most of the hostility towards Gwen is due to the Jack/Ianto, and the irony here is that she doesn't interfere with it. Gwen and Ianto are friends. Ianto and Jack are having sex throughout the show. (This is actually a Ianto characterisation problem in s1 where you're supposed to believe he goes from "I hate you and want to kill you, Jack Harkness!" in one episode to "sex, Sir, pretty please?" in the next but one without blinking. There is some clarification as to why that happened in later s2, but at the s1 time it made it impossible for me to take Ianto serious as a character) There is some UST between Gwen and Jack, but not only is that the case between Jack and everyone, but when push comes to shove in the first third in s2 and she has to choose between Rhys and Jack (and in a very important matter - this is when Rhys finally finds out about her secret job for good, and Jack orders her to retcon him, i.e. wipe his memories), she chooses Rhys. However, I'd say through the show it's clear Jack doesn't see himself in a monagamous, OTP-like relationship with Ianto (there is a time-travel episode in s1 where Jack falls for another man, and when asked whether he's in a relationship back home, he clearly says "no, there is no one"), and fandom being fandom, this is clearly Gwen's fault. Despite her not having an affair with Jack, or doing anything to interfere with Jack/Ianto.