Hello,
I know from past searches that the topic of the G1X III has always been quite divisive, mostly split into two factions "the lens is slower than the previous G1Xs so it sucks" and "APS-C is larger therefore better", but I would still like some opinions on that matter.
I have the G5X mark I and it is a great and capable little camera (with good looks, too, quite shared with the G1XIII), but more often than not I find its lens to be quite soft, particularly when shooting landscapes, not ruling out some focusing issue too. Its ISO performance is also not very good, where 800 is already quite noisy for my taste.
The battery life is quite equally bad on both models from the specs, and the G1XIII is slightly bulkier, but not by much, with the added benefit of weatherproofing, which is great for a compact, as they are usually very sensitive to everything - a friend is already on his third G7X after getting them through rain -.
I can see that most people who have the G1X III are very satisfied, and I am considering buying a used one.