However I took the liberty of testing it myself using my CRT's scanlines as guidance with a super slow mo camera, wired gamecube controller, and actually found the opposite of the OP's claim to be true - with GX having less lag on average.
I wonder if this has anything to do with the libraries it's compiled against. GX is compiled against the latest devkitPPC/libogc whereas RX is using older versions.
I've been entertaining the idea of making a stripped down "lite" version of GX/RX that removes a bunch of extra features from the main emulation loop in the interest of performance - no idea if this would make a difference though. Removing things like the turbo mode check, checking the PS3 controller flag, scanning other controller ports besides port 1, etc. It wouldn't be for everyone obviously, but could be an interesting experiment. When I do make this I'll drop a link to it here.
Like niuus said, the best way to test input lag is a Timesleuth. Unfortunately they're never in stock, and I've been on the waiting list for one for over a year now.