If a planing board is sailing as high as possible, it sails on the very edge of planing. In other words, sail the board higher and the board slows and falls off a plane. In the same way, by sailing into a lull, the apparent wind swings forward for a moment as the speed over the water is at a higher ratio than the wind speed from a moment earlier. This is the very same thing as heading up. So the board must head down to compensate. In the next moment (and this is what most everyone feels) the pressure in the sail drops and the board slows. A slower board means that it cannot point as high, so the sailor foots to keep speed up and pressure in the rig by keeping apparent wind high.
Back to the slalom/FW comparison: A slalom board can sail, say, 40 degrees to the true wind while a FW board can sail 30 degrees to the true wind. When the slalom board is sailing at its highest angle the FW is not even close to its highest angle. The lull, therefore, forces the slalom board down while the FW board keeps trucking at the same angle. Remember, lulls act as headers while gusts act as lifts.
I'm not certain about the question about no lulls at 20 knots. All wind has lulls and their existence has virtually nothing to do with average wind speed. On the other hand, if each board is tuned for 20 knots, the slalom board clearly has less range on the low end than FW kit if for no other reason than the high power of the FW board's tail and fin.
Whether you bear off to keep control or head up really depends on what angle you are sailing. Bearing off is the way to go if you are heading downwind anyway. Certainly on FW kit, heading up increases apparent wind speed and tends to force the board into a wicked round up since FW gear comes with huge "weather helm" by design. If you are heading upwind, bearing off not only points you in the wrong direction but radically increases power in the sail since turning down exposes the sail more directly to the wind. This effect is why beginner FW racers have a hard time bearing off around the windward mark.
The width of a FW board's tail always helps control upwind as long as the fin and sail size matches the wind speed. I've raced both slalom (not the new wide-board slalom racing, though), course-slalom boards and FW. I've never found sailing upwind to be a problem for FW gear -even in totally overpowered conditions. That's not the case for more narrow tailed boards which tend to bog down, spin out or blow up when sailing way overpowered upwind. Again, the harder part in FW sailing is sailing wickedly overpowered across the wind or downwind.