i think you're the one being intentionally obtuse. i've been talking about the canon G1X vs other cameras (in particular the fuji x10) just about the whole time. you said "the lens isn't any bigger than other cameras." which is simply incorrect.
your question assumes away the important differences. such as the fact that the canon G1X does have a larger lens than similar cameras, in particular the fuji x10.
but to answer your intentionally crippled question, if you hold the absolute aperture and shutter speed constant then yes, it's going to be the same.
http://forums.dpreview.com/forums/read.asp?forum=1029&message=21440105
(if you look at those pictures carefully you'll see the big advantage of larger sensors)
and in fact, i already answered that question.
http://forums.anandtech.com/showpost.php?p=32841227&postcount=22
"1x zoom" means absolutely nothing without context. a 24-70 lens and a 70-200 lens are both roughly 2.8x zooms, but they have vastly different FoVs when set to their respective widest and longest positions. no one has ever used "1x" to mean 35 mm equivalent. but guess what? the light intensity of the 200/2.8 is the same as the 24/2.8. that's why we use f-stops rather than absolute apertures, makes figuring exposure easy.
if the objective lens is the same diameter, the fov is the same, and the sensor of one camera is smaller, then you're using a larger f-stop on the smaller sensor. and that's fine if that's available. but out in the real world that's not always available. like in the comparison between the canon G1-X and the Fuji x10, for which i've already done the math and shown you that when both lenses are set to widest end and fastest apertures, the canon captures 8x more light than the fuji.
you don't seem to be able to get your head around the fact that the canon does in fact have a larger lens at the wide end than competing compact cameras.