Was he even as bad as they say?

Commodus was likely as bad as they say. Emperor Septimius Severus is said to have decried Marcus Aurelius for not strangling the kid when he had the chance. Of course, Septimius Severus's kid would turn out to be a gruesome fellow like Commodus, so he doesn't actually have much room to throw stones.

I mean, probably, absolute power and all that, but from what I hear the madness of Caligula is severely overblown since the main sources we have on him are the Roman versions of tabloids, so maybe it’s similar with Commodus.

Caligula revisionism is... very problematic. The most I would say there is that some of the pop culture interpretations of him are false, and some of the incidents mentioned as rumors by Roman historians are likely exaggerated. He was pretty unambiguously a tyrant and extremely arbitrary in his rule. If you take 'madness' as 'detached from reality', Caligula probably wasn't mad. If you take 'madness' as 'sociopathic and impulsive', then Caligula was almost certainly mad.