Both franchises are pretty terrible. Both feature bad writing with pointless diversions and lack of pacing, ham acting, over-reliance of CGI, and, at root, a fucked up worldview if you take the story to have a thesis or meaning.
It's on that latter part, however, where popular acceptance of these franchises diverge. On Transformers, if you bother to take on breaking down its militaristic, fascist literalized meanings, everyone shrugs and says, "Whatever. It's just entertainment. It's not supposed to mean anything. Why do you take giant robots fighting over city scapes so seriously?"
But Twilight, if you bother to point out the abusive, mindfucking qualities of the relationship between an old monster and a young naive girl, you'll ready get a pile-on with sympathetic men, women, and whoever else wants to join in on the beatdown. Only its major fans and a few disinterested folk will shrug their shoulders and say "Whatever. It's just entertainment. It's not supposed to mean anything. Why do you take vampires fighting werewolves over a bookish girl so seriously?"
Which is just the thing. Moral outrage at Transformers, a boys' entertainment, is considered pretentious, anal huffiness. Moral outrage at Twilight, a girls' entertainment, is a spectator sport.
Now let's get into scope.
Both Twilight and Transformers are considered big budget Hollywood tentpole productions, in fact they are considered 'phenomena', considered more than just a popular entertainment and now hallowed as a certain inflection point of culture.
But compare the following budgets:
Transformers 1: $150 million | Twilight 1: $37 million
Transformers 2: $200 million | Twilight 2: $50 million
Transformers 3: $195 million | Twilight 3: $68 million
Transformers 4: $210 million | Twilight 4: $110 million
And compare the following worldwide box office grosses:
Transformers 1: $709,709,780 | Twilight 1: $393,616,788
Transformers 2: $836,303,693 | Twilight 2: $709,711,008
Transformers 3: $1,123,794,079 | Twilight 3: $698,491,347
Transformers 4: $1,104,054,072 | Twilight 4: $712,205,856
At Twilight's highest level of support, it received only half what Transformers did for budget -- despite making far more multiples of its budget back at box office than Transformers. Dollar for dollar, Twilight was the better investment, but it was consistently given half or less what Transformers did and made less nominally in box office.
The first sequels are interesting though, because it shows Twilight coming in very close to Transformers, while operating on a quarter of its budget. If Hollywood was predominantly concerned about higher margins and profitability beyond other calculus, this would inform them that it's time to make more lower budget women-focused fantasies. Spoiler alert: they don't. "Women's movies" is still considered niche market, whereas "Transformers" is "global market."
Anyway my point is this: the smaller funded, lesser viewed, yet more profitable, more maligned franchise created the larger moral outrage over "What does this teach girls?!" whereas the larger funded, larger viewed, yet less profitable and less maligned franchise generated only academic and fussy cinephile outrage over "What does this teach boys?!"
The clear issue here being, that women have to be protected from their bad quality commercial media, which itself is rarer and far less invested in, but boys, well... it's just entertainment.
This is not an argument that we should relax our criticisms about Twilight's messaging. It's just pointing out a double standard in how media and its affect on viewers is treated depending on its target gender demographics.
And that women are so starved for entertainment that includes them that they were willing to shell out 7-10x the budget of some super shitty movies because it's one of the few series that were made with them in mind. 7-10x return on investment, Hollywood. Take that for moral outrage.