You point out that methane is far more powerful greenhouse gas than co2.  Since much of it will go up into the atmosphere anyway, we should find a way to burn it.  Assuming that was a direct substitute for, say oil, that would be helpful with respect to GHG.  

However, my question is, if you burn methane, do you end up with the same impact with respect to GHG compared to simply letting it flow unburned up into the atmosphere?

No, you get CO2 instead.
My understanding is that methane is around 23 times more potent a GHG than CO2, but is less persistent.  CH4 has a 10 or 12 year mean residence time in the atmosphere.  While I can't find a similarly simple persistence figure for CO2 right now, I understand that it's much longer - I remember reading a figure of 100 years somewhere (perhaps in Flannery's book "The Weather Makers").

I don't know the current opinions on how those two factors balance out, but I expect it won't be a simple answer given the radically different paths these two chemicals take through the world, and the complexity of the reactions they are involved in (especially CO2).

CO2 has a lifetime of about 330 years versus 7-8 for methane.  The 22x greenhouse potential of methane accounts for the difference in lifetime.  While it is in the atmosphere methane absorbs approximately 900x the energy as CO2.