...And I can give you a pretty good "lowdown" on the difference between the Jets and the Quattros...
By comparison of the Jets, the Quattros are about 2" longer and about 1.5" narrower. They are made mostly of plastic rather than rubber, which means that they aren't nearly as negative in the water.
...Which is a characteristic of the Jet fin which is truly beneficial, yet often overlooked. A correctly trimmed diver can adjust his body attitude in the water with a Jetfin... But must kick the Quattros to adjust attitude.
Imagine you're just floating there... Horizontally, and in the skydiver position. With the Jets, if you bend your knees, you'll go head-down. If you straighten your leg, you'll go head-up. The difference isn't much, but it's there... So the Jets have a serious advantage in control over the Quattros, especially for someone diving caves or wrecks where a kick might stir up silt.
Of course, if you do choose the Quattros, you can "fix" the weighting problem with some ankle weights, but that's sorta "putting a band-aid on it" if ya know what I mean.
Additionally, as you've mentioned, the Jets are much stiffer, making for precision kicks - at least much moreso than the floppy Quattros. Since they're shorter, too, they're easier to judge and retain control over the tips.
Lastly, the width of the fin actually means that there's more surface to the fin than with the Quattros (actually depending on size, but that's another issue). Frankly, I've found the Jets to be considerably more efficient at getting power to the water.
The only downside I can see is that they're so stiff that kicking a normal flutter kick is so powerful that it can tire you out pretty quickly. People not used to them complain of muscle strain and cramping. Quattros, as with many other soft fins, bend so much that they're sorta like pedaling a bicycle in a lower gear.
Anyway, your question was about alternate kicks... Yes, the Quattros do very well for alternate kicks. Frogging works well, and I'm even able to backwards kick in mine... Although it's much easier and more precise with the stiffer Jet. With my Quattros, I almost have to do these kicks in slow-mo in order to ensure that the fin doesn't "flop" and make my fin stroke worthless. Backwards kicks in the Quattros take a lot more ankle motion than the Jets in order to get them to work. This is because of the "floppiness" of the blade.
I once tried an interesting test... You decide on the validity: I put a Jet on one foot and a Quattro on the other and did a "standard" flutter kick underwater in zero vis in order to obscure direction. I swam in what I thought was a straight line; I applied the same amount of power to each fin to see if more power was produced with one fin or the other. I was floored to find that I went around in circles... Much to the favor of the Jet fin. It was like being in a higher gear with that fin.
There is one word of warning about the Jets, though... They simply don't fit everyone. The foot pocket is short and small, and I found them to be very uncomfortable. To me, this was enough of a reason why not to keep them, but I'm eagerly awaiting the new design (foot pocket) that's due out in the next couple of months. Additionally, I've found that selecting the right bootie for the Jets could solve the problem. Quattros... Well... They seem to fit everyone and are super-comfortable.
No doubt I'll be switching to the Jets soon... In fact, I'm dying to do the switch now. But I need to find the right combination of bootie and foot pocket before making my purchase.