A Snarkling has been very busy and now wonders:
And, if you have a moment, could you please advise us all on what an author's to do when they have two novels to show. Please don't be too snarky. The obvious answer would be to show the best one, I realize. I'm assuming that it is out of the question to query them both at the same time.
Well, the obvious answer, as you point out, is to pick one and run with it. The question of course is which one. I'd vote for the one you wrote second, without knowing anything more about them. I'd assume the second one is better given you'd learned a thing or two about novel writing in the first one.
You can't shop two novels at the same time to one agent, but there's nothing that says you can't shop two novels individually with a variety of agents. Send novel A to Agents 1-10 and novel B to Agents 11-20. See what happens.
Really though, I'd pick one and focus on it. And you might consider having someone with a snarky eye read both and help you pick which one is stronger.