There shouldn't be much difference in sound speaker-wise within a single speaker cab RE: parallel vs. series wiring, but the amp may change sonically. Adding another cab (parallel load) will change the sound and apparent volume level.
Ohm's law mainly dicates here. The lower the overall impedance of the load an amplifier sees, the easier it is to produce higher power outputs, to a point. Output current will increase as well. Some amps, like my Eden WT-550, can safely drive 2 Ohm loads (i.e., two 4 Ohm D-210XST cabs in parallel), and others cannot produce the current required at that impedance. Remember, that impedance specs for a loudspeaker or speaker array is an average. A loudspeaker is a reactive load, meaning impedance changes with frequency. I have old Infinty IRS Kappa 9 loudspeakers rated at 4 Ohms nominal that drop to an output device-melting 0.5 Ohms at 50hz! Not every amp can deliver the current required without blowing the mains fusees, activating thermal protection, or destroying the output transistors.
Damping factor (i.e., the ability of the amplifier to 'control' the excursion of the drivers) tends to decrease as output impedance decreases, meaning flabbier speaker response. This may be a good thing, if the resulting sound is desirable.
There are other factors as well regarding loudspeaker loading and it's effects on amplifier behavior, but I think you get my drift. FWIW, I'm an electrical engineer (power) and a hi-fi/MI/electronics nut, but I'm not an audio engineer. This is a club site not an AES forum, so there you have it, LOL!
In short, paralleling cabs will tax your amp a little more, but you will get an apparent increase in volume due to increased overall driver area and increased peak power output of the amp. Remember, every increase of 3dB (i.e, a clearly appreciable/perceptible increase in volume level) in loudness requires a DOUBLING of amplifier output power. In other words, a 600W amplifier output is NOT twice as loud as a 300W amplifier output, all things being equal. The resultant reinforcement and/or cancellation at certain frequencies with two cabs paralleled will certainly change your sound as well, so experimentation is the order of the day, LOL!
Enjoy!
Kevin