I initially considered the G/C/F to be a G/C box with an added F row, but because of the bass arrangement, it is more like a C/F box with the added G row, if the comparison to two-row boxes makes sense at all. To learn tunes typically played on G/C, in which a pulled F bass/chord figures importantly, I need to either learn the tune on the C/F rows, or learn the tune in G/C, utilizing the F row and crossing all three rows on the press to hit the F bass/chord.
The major advantage is that there are "reversals" of many notes, allowing the player to choose the bellows direction (and thus, the bass/chord) for most runs of notes in the central keys in which the box is played. There are also reversals for several of the bass/chord combinations, especially when the thirds in the chords are not sounding.
The most crucial disadvantage is that there is a steep learning curve for using the "accidentals" buttons -- the buttons with G#, C# etc. (these are the buttons closest to the chin on each row).
The size of this box has not proven to be as much of a problem as one would be led to believe by some of the predominant "wisdom" that has been posted on the internet. I primarily play one-row, Quebecois-style melodeon, and I am able to play everything from my one-row repertoire on this box. It doesn't sound the same, of course, because it is tuned in a very different way, and lacks the piccolo reeds that the Mélodie has, but the weight of the box is not an issue in relation to speed.
The only time when I wish it was lighter or smaller is when I'm transporting 2 or 3 different boxes to a rehearsal or gig!