Racing longboards plane fairly early; just not as early as formula boards. In my experience, if I can get going in 10 knots with a certain sail on a formula board, then it will take about 12 knots to be fully planing with the same sail on a longboard. I wouldn't expect much difference in the planing threshold between the 380 and the 320 (both about 2 knots higher than formula), but I would expect a slightly more gradual transition from non-planing to planing on the 380.
Of course, the main advantage of a longboard is the fact that it performs well BELOW the planing threshold as well as above it. A longboard can acheive a fast glide and powerful upwind performance even in 5 knot winds when formula definitely shlogs. As some others have said, that comes in handy when you're trying to get back to the beach after the wind dies, or you're dealing with gusty or obstructed wind.
Also, an often-overlooked feature of longboard performance is the ability to slide the mast track forward, tilt the board to leeward, and really surge on the power of the rail and the daggerboard. You may not be technically planing, but you'll be getting great speed and an intense feeling, kinda like when you're flying one hull on a catamaran. And you can do it in significantly less wind than it takes to plane.