Assume a mass casualty type situation. Something along the lines of AR-558 with physical wounds ranging from phaser and disruptor hits, to concussions, broken bones, and the like.
Each Chief would be from roughly halfway through the run of their series with whatever knowledge and experience they had at that point. Each would have access to whatever kind of portable medical kit a medical officer of their time would have brought for such a situation. There are no able bodied personnel to help. No they don’t have access to a transporter.
I think we can pretty safely put Scotty and Trip at the bottom of the pile. They’ve never shown any specific aptitude for medical work and I think 24th century Starfleet basic medical training and technology helps everyone else. Of the remaining three, Geordi seems like he would be very nice and try to be as helpful as possible about your injuries, but I’m ranking him 3rd overall. I don’t recall O’Brien ever doing anything on screen to indicate his medical competence, but we can guess that maybe he’s seen enough combat to have picked up some of the basics, so second place to Miles. Torres, with her extensive knowledge of programming and reprogramming the Doctor (enough to suggest a DNA re-sequencing of her own baby to the Doctor [Lineage, Voy]) and the fact that her year at the academy may have been a double major in engineering and medical [Extreme Risk, Voy] makes me put her in first place.
Do you think Geordi’s vision might have an advantage or disadvantage?
Yeah, now that people mention it I do think the VISOR would help quite a bit. Early on in TNG he even says he can detect if humans are lying from the minute physical changes (although the writers clearly drop that later, see his record at poker). Clearly that should be able to pick up all sorts of problems like internal temperature fluctuations and heart rate and in fact it does [The Enemy, TNG]. But what we don’t see is Geordi ever fixing those things on a humanoid on screen. So he might be better than O’Brien, but I still think B’Elanna has the edge overall. Even if my logic is iffy (and it is: she fixes the Doctor so she knows about doctoring? Eh) on screen other characters acknowledge her medical skills. Including the Doctor, who gives her genetic re-sequencing idea serious consideration before she reprograms him. Would she be a better medic than even Tom Paris, who has a lot of practice but clearly doesn’t like the work? I doubt it, but I’d probably take her in a life or death situation over the other engineers based solely on the primary sources.
We can’t have TOO many reasons to get rid of Troi…
Hmm, interesting logic; my first reaction is that even if I program a robot to hit a golf ball I still wouldn’t be any good on the links, but perhaps there’s enough medical theory that she’d have to encode that she would be the top doc. I would have expected the original program to already have the knowledge and skills useful in OP’s scenario, however.
I think all the engineers would have transferable skills, seeing as surgery is basically engineering/plumbing on living things.