[kensey]

Who is your direct manager? If it's not one of these PMs, get them involved in this conversation with both. If it is, that's whose tasks get priority. If it's "both" but one is a dotted-line report, the dotted-line PM is second fiddle. If it's "both" and both lines are solid instead of one being dotted, then your organization is dysfunctional and your best bet is to try to get one to assign tasks to you by way of the other.

I've been in this situation before as a consultant, except in my case it was PMs repeatedly scheduling me for multiple on-site visits on conflicting dates. I didn't have the power to tell either one "no", but what I did have was the power to say "I have a conflicting assignment during that time, if you want me to do this one instead, you need to get [my manager] to reassign my priorities."

Unfortunately the fact that I could make them talk to somebody else never actually solved the underlying problem of each one insisting they had the right to schedule 100% of my time, but at least when those conflicts happened, I didn't have to resolve them myself.

If your direct manager isn't willing to referee this (up to and including telling those PMs to only assign you tasks through them if they can't get their act together between them), or you don't have a single direct manager to act as referee, or you're still being held responsible for the results of both projects by managers above yours, that's your cue that it's time to look for a new position, either internally or externally.