For first-timers, I suspect the answer is always "prototype" and I think the reason is a very subtle one: a team can "gel" only through repeated full-cycle product iterations (concept, development, deployment, feedback). More loops = more chemistry.

If you have a prototype, the investor has proof that the team (what is actually being invested in) has gone through at least one full-cycle worth of developed chemistry, and is not at risk of falling apart at any point in the iteration loop. A biz guy and an engineer who haven't gone through this trial-by-fire with each other don't even know if they can trust each other, so it is kinda hard to ask a third party to trust the team. So even if the 2 guys look great on paper (right degrees, right previous experiences), the team is still an unproven quantity.

At least that's my theory of the psychology behind prototype preference.

If my theory is correct, serial entrepreneurs should be able to get away with mockups or even just a slide-deck, so long as they are able to convince investors that they can "get the band back together" and won't have to solve the people problem anew. And most serial entrepreneurs do seem to continue working with old partners in crime.

A serial entrepreneur, even if successful, who has lost his old buddies, and is proposing to build a new team, is probably as risky as a first-timer.