About the only boat that would regularly do the oil rigs is the Sea Bass. I've done one dive off one of the Es (I think it was the Ellie) off the Bottom Scratcher boat while on the way to Catalina Island. The rest of the times, it was off the Sea Bass boat.
I was lucky that all my oil rig dives thus far had been in good viz and good water conditions: mild current and low swells.
Nonetheless, oil rig dive can turn treacherous real quick if the water condition were to change. Current can easily sweep in and if you aren't good at recognizing changes in water condition, things can definitely turn nasty for you if you get swept off the rig.
Also, safety stop could be challenging because all those pillars create a lot of turbulence. One minute you can be at 15-ft, the next minute you might get pushed down to 40-ft, the next moment you may get pushed all the way up to the surface. I've learned to swallow my pride and literally hug a pillar/column for my safety stop.
Bring lights because at around 100-ft it turns into a night dive. Another issue that may come up is fishing line entanglement. I've come across several fishing lines before. I would cut them up into several pieces as far as I can reach.
I love diving the rig, but I am always apprehensive and cognizant of the additional danger.
I'd only recommend diving the rig to people who have mastered at least the basic diving skills: buoyancy control, propulsion, situational awareness, etc.