This is one of my favorite topics...

I have an asymmetric
spinnaker on a sock and a
furling Code 0, I fly both from the
bowsprit. This season in particular we have done a lot of practice with both of them, shorthanded, single-handed, and with full crew).
Here is my experience (I understand the Code 0 is technically an asymmetric, but here I call "Asymmetric" the asymmetric spinnaker only).
Asymmetric spinnaker with sock. Initially, we did not like it too much because the sock had a tendency of getting stuck on the forestay in the jibes (this may be specific to my boat, since there is very little room between the spin
halyard and the top of the forestay). However, this problem is solvable by improving the timing of the jibe and a few other tricks.
Overall, we now see the advantage of the sock when shorthanded or single-handed. With full crew, it is really a wash, because an asymmetric is not that difficult to handle the "conventional" way either, even in high wind (i.e., no sock, directly in/out of the bag).
Furling Code 0. My experience with the furling Code 0 is very different. Since it flies from the
bowsprit, it has to be rigged on the
dock and is kept aloft throughout the outing.
The big problem with the furling Code 0 is that the top of the sail tends to unfurl on its own the moment the wind increases. The leech of the Code 0 is rather full and does not furl tightly, so it potentially catches wind and unfurls no matter how careful you are. This problem is exacerbated in the Code 0 I have, which is cut rather poorly (I'll have it recut this winter), but is intrinsic to some extent to the shape of the sail, which has a full leech by definition). Once the sail is partially unfurled, you have no other option but to unfurl it completely and then furl it back, which may be annoying to do if you are going upwind in high winds (that's when the unfurling happens). In high wind and single-handed or short handed, the situation can easily degenerate into a battle with the Code 0 (the furling drums for Code 0, even the best ones, are relatively primitive and have a tendency to
malfunction if there is stress on the furling line or the torsion line). In one occasion, we ended up having to take the sail down the "conventional" way rather than furling it. In that situation, the sail is much more difficult to handle on
deck than a conventional
jib, because the rigid luff does not allow to flake it as you would with a
jib.
Overall, I have to say, unless you are an ultra-competitive
racing sailor, I question the usefulness of the Code 0 if you have an asymmetric with a sock. The Code 0 covers some angles that the asymmetric does not, but also has a narrower wind range and does not do as well in the angles were you can fly the asymmetric. In general you'll fly the asymmetric much more. You are much better off having a larger
genoa or having two asymmetrics (for example, one for low wind and one for high wind). If you have to choose only one flying sail, the Asymmetric with the sock wins hands down.
I'll have my Code 0 recut and give it one more try, but overall I would not recommend a cruising furling Code 0 (one of the high tech, extremely expensive
racing Code 0, especially the new ones without a rigid torsion line, is another story, but the cost is not justifiable unless you are an ultra-competitive racing program).