Gelman does real, solid work and confines his righteous takedowns to a side hobby. And his criticisms are directed at individual, specific cases, with evidence, and he reserves most of his wrath for repeat offenders rather than one-off mistakes, which are unavoidable given enough projects. He confines criticisms to his area of expertise, which is statistics.
Ioannidis' claim to fame is writing a hand-waving, philosophical argument in order to cast doubt on all research at once. Followed up shortly by a paper that implied (but didn't directly state!) that regression to the mean on replication implies error or fabrication in the original. And he has ridden this sort of tired argument into a lucrative and prestigious career and Stanford appointment. Never mind the collateral damage on funding and morale. My theory is that people pay attention to Ioannidis and wring their hands about these highly generic issues for the same reason most people pretend to be highly, highly concerned about sexual harassment/discrimination in the workplace -- they're praying that if they act concerned enough, the hammer will fall somewhere else. But indiscriminate criticism like this is highly toxic to science (or anywhere else, for that matter, and has the side effect of letting real bad actors off the hook).
A further moral of the story is that, for better or worse, I don't trust and generally ignore criticisms that do not come from someone who has invested time into a field and made useful contributions to it. 'Full-time critics' strike me as generally sleazy and opportunistic, and I doubt the sincerity of their desire to 'improve' a field if all they can do is tear down others' work and not provide any of their own.