Comparative or superlative to describe a quality of a member of a set of two things?

For example, 'he's the bigger of the two guards' or 'he's the biggest of the two guards'?

The comparative indicates that something is bigger/more difficult than another member. If there's only two members of the set being described, then surely both forms are equivalent?

What about when the comparative and the superlative aren't regular? e.g., 'my puzzle is the more difficult of the two' or 'my puzzle is the most difficult of the two'?

I think I'd probably use the comparative, but it seems logical that the superlative would be okay too.

Weird. Here's a typical usage chart for XXXer / XXXest of the two with heavier/heaviest...

The same general pattern shows with older/oldest, larger/largest, etc. At some point in early C19, the superlative -est form starts to fall out of favour. Although it doesn't sound terrible to my modern ear, apparently these days we don't normally say something is the tallest of the two. The Google Books estimate in that link is totally unrealistic (there are only 27 instances, mostly old) but I'm prepared to believe there really are 44,000 instances of is the taller of the two as claimed.

What strikes me as particularly odd is that "irregular" worse/worst barely shows the effect...

I don't know why that change occurred a couple of centuries ago, but I consider it significant that worse/worst has been least affected, and better/best (also considered an irregular adjective) changed later than the strictly regular forms. My guess is that people who were less "schooled" (in logic, grammar, etc.) simply didn't bother making a special case for this particular comparative with only two candidates. Until education became more widespread, with more teachers telling more pupils to be more logical, and use the "right" word in such contexts.

But the reality is we don't apply this logic consistently. I suspect worse/worst is more resistant because it's not so obviously the pattern teachers (or our own "inner logician") rail against. But consider a context where the "only two candidates" aspect is less overt...

Kidnapper: "I'll let you go if your parents pay a ransom. Give me their phone number"
Victim: "They divorced years ago. Which parent's number do you want?"
Kidnapper: "The richest [one], dummy!"

I know the dialogue's a bit crummy, but I certainly don't think changing it to richer would help.

TL;DR: It's just "grammatical logic" telling us not to use superlatives where comparatives would suffice. But we don't tend to do this so often unless the actual words (as opposed to the semantics or "overall utterance context", for example) make it glaringly obvious.

"Bigger" would be natural when comparing only two, "biggest" when the set is larger. Likewise for the "more difficult/most difficult" case.