Here are my two G-cases. The white sunburst 3-6-9-12 dial with gold hardware is manual ref 135.041 cal 601, and the black/grey(?) dial is ref 166.041 automatic with cal 565 (caveat emptor, it's yet to be serviced and I haven't opened the caseback, but pretty sure<tm>).
I'm a dress watch guy so these fit right in. And at least for the 135.041, I can attest that for me it is a very nice, light, casual all-arounder.
Notice on the last photo how much thinner the manual 135.041 is (~ 8.5mm vs 11mm); but also automatic 166.041 doesn't have original crystal so that might add to the height.
Coincidentally the one with the gold hardware is the watch that dragged me into the rabbit hole that are Omegas. And that only last summer, which feels like ages ago.