The release of a large amount of methane is the only plausible explanation for the large shift observed in stable carbon and oxygen isotope ratios at the PETM. There are references to publications by Katz (et al.) that might provide an explanation for the cause of the release. It seems clear that the ultimate cause of the methane release is unclear, but it is clear that the methane release followed by oxidation to CO2 is what actually happened.
Anyway, this release of methane seems speculative and not a good indicator for what could happen with our current release of CO2.
Both methane and CO2 are greenhouse gases that change the Earth's radiative balance if their atmospheric concentration changes. Provided that a methane release and oxidation to CO2 is what happened at the PETM (and that's what "fits the facts at hand"), then the PETM shows that greenhouse gas increases in the atmosphere can drive a warming trend.
As other posters pointed out, methane is a much stronger GH gas. They change the radiative balance in different ways, increases in CO2 have less effect as the overall concentration increases while methane has more as well as being 20 times more heat absorbent at current concentrations. In short, rapid rises in methane could cause warming but rapid rises in CO2 would not without the forcing mechanism causing rises in water vapor. We've talked about forcing before and I will say it again, forcing is a figment of a model and a theory, yet to be proven or demonstrated outside of a model.