If nothing else, it's likely that a Fox editor would pull an unflattering Trump photo and vice versa. It's hard to imagine an intentional process for making the other side look bad (can you imagine a meeting where that is decided?), but what I described is an organic way in which a systemic process could arise.
I don’t know how it would come about, but on Ars Technica’a articles about the Republican Party, they use pretty unflattering photos, and I’ve seen many articles from conservative sites using unflattering photos of Democrats.