Statistically speaking, if you follow a checklist you are less likely to die. However, the complexity of the task will dictate the amount of steps, or whether one uses a checklist at all.
For OC I treat every step as its own entity so I don't really have a rigid checklist, but each individual component gets its own thorough operational check. The pre-drop briefing takes care of the rest of the gear checks as I'm doing a bubble check, flow check, DTGPg, head-to-toe check with my team, of which things like breathing from each regulator and inflator/opv is part and parcel to validate my rig as well as my buddies. Of course all of this has been checked on an individual basis during setup, and validated with the team. There may be sub-routines in those checks but not significant enough. Now I tend to do things the same way each time as I am a creature of habit, and rarely does it deviate from the pattern, so it definitely helps being a little obsessive compulsive.
It's much easier to perform individual checks on OC, so unless it's a serious dive, mental checklists are enough. For CC however, there is much more than can go wrong that cannot be instantly corrected so a rigid checklist is absolutely required. Since there are failure modes that you cannot distinguish until it's a serious issue, it's not something for which you want to rely on your memory.
Quite literally an OC checklist would be like:
1) Drysuit check.
2) BP/W/Tanks secure & analyzed
3) Regs attached, dry leak check, pressure check
4) Inflator/OPV check
5) Gear up & computer check
6) In water bubble check, flow check & head-to-toe
7) Final briefing & descend
On a hot drop you might not get the chance to do any in-water checks so you will have to do as much as you can on the boat. However, the more comfortable you get the more it becomes ingrained and the less you are married to an individual sequence of events. Not to say you become complacent, although some people do, but it's more akin to doing an S-Drill whereby it becomes second nature and instead of actively having to command every maneuver, you are unconsciously doing things like checking to make sure your buddy has his long hose clipped off before swapping your can light and deploying the long hose. (Yes, an S-drill should be part of every dive)
A recreational checklist might only consist of "Leaks? Gas? Stuff works? Fall off boat." Much more complacent, but typically much less risk.
Alternatively, here's an example of a CC check for a Megalodon rebreather. You can see the importance of following it to the letter.
Meg Checklist
In the end it's up to you to decide whether or not you need a rigid checklist to safely accomplish your dive. I have concluded that for OC, my mental checklist is perfectly adequate for all but the most risky dives.
