Honestly, the GCHQ does seem a lot more brazenly nefarious than the NSA. A lot of the shit that comes out of the mouths of GCHQ spokespersons, shows open contempt and disdain for civil liberties and due process. At the NSA, it's more like they just don't respect those things, or think fighting terrorism/drug cartels/flavor of the month, is more important.
If I could choose to dismantle one or the other, I'd go with the NSA, but only because it has more capability. I definitely wouldn't want the sons-of-bitches in charge of the GCHQ, running the NSA.
They show contempt for civil liberties but claim to operate within the law. Since GCHQ is specifically mentioned (and pretty much exempted) in most surveilance related laws this seems plausible.
There is weakness in the oversight that GCHQ is supposed to have.