Two different outputs from same type of IC's
You seem to expect that each exemplar of a particular chip type behaves the same, but that is a misconception. What you can expect is that each exemplar behaves within the specifications guaranteed by its datasheet (if you use it within the limits that are also stated in said datasheet).

(But take care: different manufacturers might produce chips with the same type number, yet the each have their own datasheet, which might not fully agree!)

For the TI L293D the relevant part of the datasheet is shown below.



It states that the maximum voltage drop (for a current of 0.6A) over both the high side and the low side of the output drivers is 1.8 Volt. Note that it does not state a minimum, so the drop voltages you observe are all in accordance with the datasheet.

Side note: strictly speaking these values are valid for Vcc2 = 24V only, but it is likely that they apply for other reasonable Vcc2 values. The fact that the datasheet mentions these figures for 24V only is an indication that this chip was never meant for low voltages, and indeed it doesn't perform too well at lower voltages. But it is cheap and widely available...

PS the D after the L293 only means that the chip has built-in freewheel diodes. It has nothing to do with the voltage drop of the drivers.