(jlpicard - we have several bobs here, but without being presumptuous I'll say a few words anyway - firstly, that it's nice to see aaaaarghboy back here again! And secondly, this is way too long, but now I'm too tired to prune it down...)
It feels to me like we are bouncing around at least three or four completely different factors in this discussion, and as a new reader I would be pretty confused about why (though not whether) Series electronics sound different from Signature.
1) The most important difference (other than cost) between Series electronics and everything else, is the pickups themselves. Series are single coil, the others are humcancelling.
By itself, the tone you get out of the Series pickups before any other electronics, vs. the AXY/MXY/FatBoy pickups, will be the biggest difference. Having never had a Series instrument in my hands for more than a few minutes at a time (and only a couple of times at that), I'm not the best one to characterize this, but many others here have tried.
I'm still a little fuzzy on the distinction between hum-cancelling vs. -bucking, and why it matters whether you can coil tap them or not. And yes, the AXY/MXY pickups have a smaller magnet/aperture than the Series, but the FatBoy uses the same larger magnet size as the Series - and I believe I have read that this was in an attempt to get closer to the Series sound, without the expense (but it's still fundamentally different, since it's not a single coil).
Regarding the power (9 vs. 18 volts), I really don't think this should be interpreted as suggesting that the non-Series instruments have limited headroom. Rather, the Series circuitry is sufficiently complicated that it sucks more juice, and/or maybe you just need it to properly handle the single-coils. I'm out of my element here, but I have to believe that if it would make a huge difference to throw an extra battery in the non-Series instruments, then it would be there.
2) I'm nearly certain (just short of stating it as fact), that aside from the Q controls, the filter modules are all the same - whether it's Series, or a non-series with one or two filters, or even an SF-2.
I believe that whether you have a two or three position Q switch, and what exactly the dB settings are in each position, is mostly a matter of parts values (resistor choices and stuff). You'll get more or less Q, more or less settings, but it's all the same stuff, not fundamentally a different circuit.
The Really Big Deal is the CVQ case. As far as I can tell (mostly by guessing), it takes a lot more of Ron's time to build one of these things, which is why they aren't generally available unless you order Series II electronics. Even then, the relatively modest upgrade cost from Series I to II probably doesn't cover the effort, but as long as you're in that deep...
In regard to the original question, whether you have a CVQ or a switch is really a separate issue, and not to be confused with the difference between Series electronics and the others: i.e., a Series I does not have CVQ.
3) How many volume knobs do you want? At the very least, you can have a separate volume for each pickup; those two plus a master; a single volume plus a pan; maybe throw in a pickup selector switch.
We've had some discussion about volume/pan versus separate volumes (not convincing, in my opinion), but again, this is a totally separate issue from the design of the pickups. I think all of these work well, and it comes down to mostly a matter of personal preference, not something that fundamentally changes or limits your tone possibilities.
4) How many filters do you want? This is probably a case where if one is good, two are better... but Signature gives you two, so that doesn't matter in this discussion (and thankfully, we don't have to get into the difference between a filter and the simpler tone controls, repeatability of settings, etc.).
5) As for the hollow body effect, I think keavin and I have graciously agreed to disagree on this matter. I'll still argue that the empty space is not sufficient to give you an acoustic effect, though I can believe that reducing the body mass may have an effect on tone. More likely, however, it's the Series pickups themselves, and/or more extreme use of the two filters.
To sum up (sorry for carrying on): regarding the original question, the key difference is not the number or type of controls, but the fact that one uses Series pickups and the other doesn't. That will make the biggest difference (assuming identical woods, strings, scale length, fingers...).
At the same time, that doesn't mean you would be disappointed with the sound of a non-Series instrument. It depends on what tone you are looking for. There probably is a special sound that just plain requires Series, but then again we have an awful lot of people here who are perfectly satisfied with non-Series, myself included.
The best thing to do would be to put aside the tone control configuration, and try to listen to the different pickups.
-Bob