And sometimes there is no definitive answer since it depends a little
on the guard at the door.
Yep, that's the problem. If you, say, google pictures of tourists inside the Vatican Museums, you see some of visitors wearing skirts or shorts above the knee or hauling bags that should be considered too large. They don't post max. dimensions so it's a crapshoot, and what some guards will apparently allow through, others won't. I'd go with the smaller size of the bag to take the least amount of risk.
I've my doubts that even the smaller one will be allowed on the scavi tour but I've not done that one so.... I will say the smaller, the better in the heavy museum crowds. Personally? In crowds, I'm more comfortable with a cross-body bag that I can swing around to the front to access things I might need to get out of it versus have to take a bag completely off to get inside it.