I spend quite a bit of time on both styles.
I mainly fly Ozone Edges on the snow for the upwind advantage on terrain and for more time in the air gliding or bigger boosting. I also fly Ozone C4's on the water and when I'm on the flats snowkiting for the unhooking.
I find that both kites obviously work for both schools. But the most drastic difference I see are these 4 things:
Slack...Once you pop and your lines slack, the C4 floats in the same place for longer without input from the bar. It'll almost ride along driving itself. The Edge will fall towards the water much faster with slack in the lines so you have to hurry and turn it up.
Trimming... I can ride unhooked, pop, whatever an entire session without trimming for anything but wind strength on the C kite. But I'll trim my Edge to unhook every time I do it. Otherwise it'll waddle back into the power zone backstalling or if powered it'll pull too relentlessly.
Crashing... I also think that as a kite smashes into the water straight and hard, the c kite has more contact with the leading edge to the water so the kite often hits more evenly. Where the race kite's contact is narrower in the center putting lots of pressure on the canopy and center strut as to tear the kite in half or at least stress it.
Down wind... the C kite has a nice easy feel, especially unhooked. I think the leading edge squares up to the wind with more wind resistance, so as the kite gets to the edge of the window it hits a wall and resists overshooting. Therefore it blows back to where you need it naturally. This plus the large surface area wingtips give it a great luffing feel so you don't have to pay as much attention to it while you ride downwind. The Edge is fast down wind, but you're making it happen by flying aggressively.
Make sense? Probably TMI, but it's how I feel you know?