I have a mild interest in Frenchrifles but probably can't help a whole lot. I would say the least collectible if the "mystery rifle" If you don't know what it is, hard to collect it. Pros on the G is that is most likely saw combat against the Germans. Some collectors would put a premium on that one over the H that appears unused. Con's are worse condition than the H which for others would put the H on top. One thing to make sure of is that the H is original finish and not a post war refurb, that would push the G easily in first. Personally I'd go for the G given the choice. I prefer rifles that have some history. I have an unissued No 4 British
rifle and I really don't know what to do with it. Yes it's worth a lot of money but it just doesn't do much for me other than amaze me a bit with all the teeny markings you never see on used rifles.