Note that the Peter Principle came long before the Gervais Principle. It might be more true to say that the Gervais Principle is largely a restatement of the Peter Principle.

I think they are related but focus on different things. The Gervais principle talks of losers, clueless and sociopaths (with a focus on the latter), not something the Peter Principle deals with. I'd say the Peter Principle deals mostly with what the Gervais Principle calls "the clueless".