Methane doesn't stay in the atmosphere nearly as long which means that, in theory, it would cause some short term warming, but then the methane would break down and we would slowly return to more normal levels. There are alot of unknowns, and while a very worst case scenario involves runaway methane causing warming, we don't know how likely this is to happen. We do know that CO2 takes hundreds of years to dissipate and will cause the ice caps to melt which will lead to higher sea levels overall.

IPCC does consider tundra, methane, feedback loops.

https://www.ipcc.ch/publications_and_data/ar4/wg2/en/ch4s4-4...

Citations elided:

"Arctic and sub-Arctic ecosystems (particularly ombrotrophic bog communities, see Glossary) above permafrost were considered likely to be most vulnerable to climatic changes, since impacts may turn Arctic regions from a net carbon sink to a net source. Literature since the TAR suggests that changes in albedo and an increased release of methane from carbon stocks, whose magnitudes were previously substantially underestimated, will lead to positive radiative climate forcing throughout the Arctic region."