there is no difference in sound quality of a S4, D2 or D4. the voice coil configurations are only to ease the hookup of a sub to the amp. for example
an S4 is a single coil of 4 ohms. almost all 2/4 channel amps are 4 ohms bridgeable. so you can hook them up with a 2/4 ch amp easily.
a D4 is a dual coil sub with two voice coils of 4 ohms each. each voice coil handles half of the total load on the sub. so if a particular S4 e.g. has a single voice coil that handles 400 watts rms, a D4 will have two that handle 200 rms each. total watts will be same, output will be same. but a D4 can be hooked up at either 2 ohms or 8 ohms. this comes in handy as many of the branded monos are only 2 ohms stable. OR it comes in handy when you are using two subs. so you can bring the total impedance at 1 ohm and give decent power to both. (a 1 ohm stable mono amp will give most power at 1 ohm). you can also hook 2 D4s at 4 ohms total impedance but that happen when the amp gives enough juice at 4 ohms.
a D2 can either be hooked at 1 or 4 ohms. in a way, as a single sub, D2 would be the best option to get as, when you are in a tight budget, you can hook it at 4 ohms to a 2/4 ch amp and later get a mono and use it at 1 ohm. for two subs, the hookup will be at two ohms.
so if you have a 2/4 channel amp, get a S4 or D2
if you have a mono amp stable upto 2 ohms and gives enough juice for one sub (at 2 ohms), get a D4
if you have a mono amp stable upto 1 ohms and gives enough juice for one sub (at 1 ohm), get a D2
if you have a mono amp stable upto 2 ohms and gives enough juice for two subs, (at 2 ohms), get two D2 or two S4
if you have a mono amp stable upto 1 ohms and gives enough juice for two subs, (at 1 ohm), get two D4
above of course is just an example. there are other options available but this is just to give you an idea.
lets suppose a sub is 400 watts rms and has S4, D2 and D4 versions.
S4 getting 400 rms from a mono amp at 4 ohms will give same sound as D2 getting 400 rms at 4 or 1 ohms and that will be same sound as D4 getting 400 watts rms from an amp at 8 0r 2 ohms.
the difference in sound, if any, will be because of a particular amp's ability to play clean music at a particular impedance.