Gennaker is a confusing term because it is defined differently depending on where you live. In Europe, apparently, it is how they refer to an asymmetrical spinnaker. In the United States it usually refers to a "reacher," more like a VERY large jib made of lightweight, spinnaker material. It differs from a spinnaker in that it has a luff wire, and usually it is roller-furling. It is used like a spinnaker off the wind; but because it is cut flatter than a spinnaker, it can be also be carried going to windward in light air.
It is more versatile than a spinnaker and is much easier to use because of the roller-furling.
The best-known brand names for beach cats are "Screacher," which was designed by Randy Smyth, and "Hooter," which was designed by Dave Calvert. But all sailmakers make them, regardless of what you call them.
As far as I know, the only objections to using a "reacher/gennaker" as opposed to an asymmetrical spinnaker are that:
1) the reacher creates too much windage when it is roller-furled going to weather;
2) when the reacher is furled, the weight aloft makes it harder to right the boat when it is capsized.
I agree with No. 2, but as far as the furled reacher causing too much windage, I find it difficult to believe that those huge snuffer bags don't cause a lot of windage, not to mention waterage (is that a word?)
