Each configuration has advantages and disadvantages that you have to consider.
The Sziklai configuration has voltage gain, whereas the Darlington does not.
I find this is a disadvantage in that the hFE of the two transistors right out of the box can vary widely and hFE droops at high collector currents - so your voltage gain varies a lot, just for the Sziklai stage. This makes stability harder to obtain with overall loop feedback, because the gain drops under load and increases at light load. Your circuit must be carefully designed and it can work fine. It's just an extra hassle.
I no longer see them used anymore in discrete audio power amplifiers. I think because changing transistor manufacturers or part numbers can cause problems. Hobbyists can measure and select the hFE for each part but that luxury is not practical in production.
Another trap of the Szilaki is the parasitic oscillation at several MHz that can show up and ruin your day. The mechanisms for this I don't exactly know, IC's have it from the low hFE lateral PNP part. You can't have a lot of flying leads (parasitic inductance) in their construction.
Input ripple modulates the (emitter) of the driver transistor which gives a bit less PSRR. A few audio amplifier authors say the configuration is slower due to the voltage gain.
So a Darlington pass transistor has poor voltage efficiency, you always lose several volts there but it's much easier knowing its voltage gain is always around 1 and your overall loop feedback amount stays well behaved.
The Tiger and SuperTiger had some stability problem, I recall a hand written note from the the designer making a few mods to fix them, after a friend went into business selling them and almost went broke because they were unstable and cooked output transistors.