The scenario would dictate the actions you might take.
If you had an engine fire at V1 that was unextinguished then you would want to LAND ASAP with either a visual circuit or short radar vectors. The firefighting is done and the priority is landing.
On the other hand if you had unidentifiable smoke on as transpacific route ETOPS 180+ then the priority would be fighting the smoke/fire via an unwieldy checklist as it’s your only chance of survival bar ditching in an ocean.
In the first scenario it would be sensible for the skipper to be PF and demonstrate their finely honed manual handling skills after all these years to land as quickly as possible.
In the second it would be sensible for the FO to be PF and monitor the AP in the cruise and for the skipper to carefully run through every item on the checklists.
Also it’s useful to bear in mind that some items can be modified or dispensed with entirely. For example on the EFATO scenario the pax/crew are already secure for take-off so a NITS/PA can be dispensed with or done over the PA via a brief alert call.
Also briefing for an approach when you are downwind to land can be superfluous too - would you delay landing to finish talking about landing? (Although I have seen that in the sim
)