Diffrence in class a and class ab, mainly is the biasing, with class ab its bised to be just turned on. Thats great, low power consumption for same or simullar perofmrance.
But once you put music into it, for example a sine wave, theres the top upper postive and bottom negative swing, with a 1HZ sine wave, the npn will be turned on for 0.5 secs and pnp will be turned on for 0.5 secs when the npns are turned off.
Heres the concern, as npns and turned off and pnps turn on(Not excatly tunred off but one side has a higher biasing), it creates distoriton. It not only creates distortion but also changes the dc voltage at speaker, it will varry more, not zero volts any more.
with class a, since its biased to maximum or near maximum, all devices are turned on no matter what you do, and turned on with the same ammount of current voltage.
Therfore has less distortion and more stable dc voltage at speaker and has better sound
A good amplifier should be APERIODIC, with high PGW. Not a low pass filter. The amplifier class A are more aperiodic with less stage and less or NO frequency compensation. The PGW is higer hence the sound is better. for good amplifier class A with NO frequency compensation see this link 2A & DIY
The question is: What kind of driver efficiencies are we talking about?
It is often assumed that you can get away with much smaller power for the tweeter vs. the woofer (and hence Class A etc.), but that requires a typical setup where the tweeter might be at >100 dB/W/m and the woofer at <90. If all of them are about equal, surprisingly large peak power headroom may be required in the tweeter amp for accurate reproduction of certain transients (e.g. snare hit).
It does make sense to have a "nice" tweeter amp, with low crossover distortion. The bass amp can be almost anything assuming it has enough "grunt" and low output impedance.
I recommend looking up P3A discussion on recommended transistor types and biasing, e.g. here.