Question: Between a mains step down transformer and a SMPS, which would be safer for a bench power supply? I cannot look inside the transformer in either case to judge the insulation quality. But, if the insulation does fail there would be 230VAC at the secondary for the mains transformer. And, maybe 325VDC at the output of the SMPS (is that possible)? I can visually inspect the SMPS PCB to check if there is proper clearance, presence of MOVs, thermistors, fuses etc, but of course cannot see inside the transformer.

So the question is, which is easier to make safer (or screw up)? Which is easier to figure out when new, if failure will be catastrophic in future? Can SMPS transformers fail due to failing mosfets etc? I'm guessing that if a mains transformer works without issues when new (including the problem of interwinding capacitance), I can expect it to work for at least a decade without issues, right? Assuming everything will be fused properly and fan cooled.

It's one thing to get a shock from inadvertently touching bad wiring, and quite another to be exposed while clutching the wires in my hands. So I am concerned somewhat about safety. Of course, an RCD/RCCB should probably be put in, but I don't have that yet.

[PS: I'm planning to put a buck converter and then a linear regulator to drop and adjust the final output voltage, be it the SMPS, or the mains transformer.]

Answer: 
Voltage is not a reliable indicator of charge state. 

Both batteries can have a terminal voltage of 12V, but one be half charged and the other nearly dead. Running them in series will work until the weakest one is completely discharged. 

At that point, the battery that still has charge begins pushing current through the discharged one. This "charge current" is running in the opposite direction from the current when the battery is being normally charged. Sort of like if you connected a 12V battery charger to a battery backwards.

This "backwards charging" will usually destroy the battery. This has happened to your battery. A discharged battery will usually show some voltage. Yours is showing 0V, so it is shot.
The battery connected to the positive terminal will drain first every time. The idea that they drain evenly is incorrect. I check my trolling motor batteries for voltage every time I bring my boat back from the lake. The one connected to the positive lead is low and the one connected to the negative lead is 12+V.