Gaming on an External Display in the Retina MacBook Pro

Can someone with a 15inch Retina MacBook Pro answer the following question:

Does the gaming performance improve if you attach it to an external 1080p display?

I'm planning on buying a 15inch Retina MacBook Pro, for personal+work use, however I'll like to sometimes attach it to a bigger external display to watch some movies, and gaming.

I wonder if the gaming performance improves if instead of pushing 2880x1800 pixels in the Retina Display, it only pushed the 1920x1080 in my 40inch home tv display.

I'm not a hardcore gamer, but I do enjoy some gaming, and was hoping to buy the Retina MBP as my only computer

Thanks!