There's a substantial difference in price, though in the US I've seen the Fuji Ace listed at nearly $400.
I'm expecting this bike to endure about four years of use between my two sons. The most obvious differences I notice are the handlebar configurations.
The gear shifter on the Louis Garneau are more like the old school style I remember as a teen, located on the top tube. I wonder if that might be a bit distracting for such a young kids vs the grip shifter on the Fuji.
The Garneau has a front deraileur, the Fuji doesn't. Not sure if my kid will require more than 7 gears.
In short, it looks like Fuji has taken a KISS approach for a child's first road bike. I've seen the Garneau 24" in person and it's quite slick.
Two things jumped out at me - the shifters and the chainrings.
1) Chainrings - You mention that 7 gears may be enough and you may be right. However, the gear range is vastly different due to the single ring on the Fuji being a 40 while the LG has a 46/35. The LG has more fast gears AND more climbing gears. I could see a kid start out using primarily the 35 tooth chainring and growing into the larger one as they got stronger.
2) Shifters - Depending on your kids' hand strength this could be another win for the LG with the old style shifters. Many kids (including mine) have trouble with twist shifters like on the Fuji. Not everyone of course but a fair number of kids end up with after-market trigger shifters instead. My oldest rides a Felt F24 road bike and even on that we installed triathlon bike shifters in the ends of the drops. While it is an odd place for the shifters to be located, it works easier with his hand strength and range of motion. Something to consider.
My thoughts - based on my 9-year old's Fuji Ace 650c - upgraded to Sora STI levers...
* A single chainring will be easier for your kid to figure out. My 9-year old still doesn't understand when he should be on the big or small rings. It's really aggrevating when he's grinding the front deraileur and doesn't know the concept of cross shifting.
* Mountain style brake levers might be easier to adjust so small hands can reach them. My 9-year old can brake OK when he's in the drops, but he can't generate much braking force from the hoods.
* $600 is a lot of money for a bike that will be outgrown pretty quickly. If you think you could re-sell the LG and recover some of the initial costs when it's outgown, maybe it would be worth it.
The shift lever location on the LG doesn't look very well thought out - especially if you want grandkids.
That being said, that LG is an absoulutely gourgeous bike - tough call.