Are the wall warts different? Can you post photos?
Wall warts can have conventional transformers, which are quite large and heavy, and the input voltage will be just 110 / 120 or 220 / 240 V. They will never handle a wide voltage range unless there is a switch to change the voltage.
Wall warts with conventional transformers can have:-
AC output.
DC output, unsmoothed
DC output, smoothed
DC output, smoothed and regulated.
Alternatively, wall warts can have high frequency transformers, which are small and light, and usually the input voltage covers a wide range, such as 100 - 240 V. They always have a DC output, smoothed and regulated, but the quality of that smoothing and regulation can vary.
You regulator may need a minimum capacitance on its input to stop it oscillating.
Capacitor selection can get very involved, and so a simple equation risks being an over-simplification. As a guide, 10,000 μF per amp of load is a good start. You may be able to go smaller with more careful consideration.