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I probably do use my RX100 at its widest 28mm equiv probably 75% of the time at least (pretty much I'm either zooming in all the way, or shooting wide) so probably wouldn't miss the zoom that often, though it can occasionally be nice to have.
Focus is a little faster, it has OS (though not the best good for 1-2 stops maybe) and a few cool modes that actually work really well such as sweep pano and watercolor. The RX100 does make for a fantastic video camera too.
GR of course has the larger sensor so should be better at higher ISO's (offset a little by the f1.8 on the RX vs f2.8 on the GR) and just a really well designed interface. Its more of a true photographers tool, than something that tries to have a little something for everyone, snapshot masses included.
GR also can take the GW3 (if I can ever find one) so having that 21mm equiv is a big bonus, though it would kill pocketability.
RX100 is nice in that it can share batteries with my RX1, but the GR is also nice because it can share batteries with my Sigma DP2m (so I've got a real charger for it too, none of that USB in camera silliness way too many cameras require these days)
Sony is a little cheaper, and already paid for, GR is still a great value at $799.
Somewhat tough call as it would be a bit redundant to carry them both, much less keep them both, because if I'm grabbing the RX100, then whats the point of another $800 "pocket" camera left at home. Likewise, if I take the GR, then whats the point of the Sony still as it still has pretty good resale value to recoup
Our state fair is in town so perhaps a trip to the fair carrying both of them would be a good test for if I feel I miss the zoom, if the focus keeps up, and/or if I find snap focus useful, and if at night I see better results from the GR
Its too bad the GR couldn't of been a f1.8 lens, as then it really would have a real edge over not just the X100 but most any APS-C compacts. Would be a real no brainer.
As it stands, it seems a very good lens, quite sharp edge to edge, but its pretty limited in getting much subject isolation, which you'd expect from an 18mm f2.8. That does factor into my preferences a little bit, being spoiled with the 35mm f2 on the RX1's FF sensor.
GR seems like more of a documentary/street style camera though, meant for showing the full scene, not so much creative isolation with razor thin DoF like the RX1 often leads me to shoot.
All and all though, I'm really impressed with the GR as a whole. Its a really unique product in a very crowded market with a really nice size, great ergonomics and a very, very competitive price.