They're basically WW, SM, and Batman transformed into larger-than-life iconic god versions of themselves with far increased power (in a way that reflected their specialties) who ruled their own universe.
Ah, that's pretty hard to say, they didn't exactly fight with other cosmics.
Also their powers are thematic. For example, when Enigma stole Batman's power as part of a lesser trinity (before the real Trinity achieved these trinity forms), he talked about cloaking the world in eternal darkness and making himself insubstantial so he could never be brought to a battle he could lose when he wanted to make Morgan Le Fey (who had taken WW's role in their fake trinity. They didn't have a SM so were thus both substantially weaker than the full trinity) back down when she looked like she was going to destroy all life on Earth instead of finding a third so they could reshape it like he wanted (Morgan could reality warp wide areas, but with the incomplete powers life didn't survive the process).
Supes did manage to somewhat fight with Krona, with Krona claiming he has about a third of his overall power.
Hence, the entire Trinity was able to depower him, at the cost of their godhood.
Outside of combat, the Trinity reality warped the universe. (It would have to be more then merely Earth, as events like the GL's coming to Earth were altered as well, along with the GL roster.)
Plus, Superman affected Tommorow Womans status as an alternate timeline character threatening to fade away, into a mainstream character who's entire history is included in the main timeline as if she always existed, and even made her into flesh and blood.
Also keep in mind Joker and the evil Trinity were warping time and space, and they had a mere sliver of the creation energies the iconic Trinity had..
I'm a Marvel fanboy so the most I'll say is that WWH doesn't want to lose his mission whatever mission that may be so if getting his brains beat in is his mission then nothing is going to stop him, no matter who you throw at him.