The legal way of logging hours depends on your licence. ESASA licence means EASA rules, FAA licence means FAA rules.
You can be a PIC under FAA and not a PIC under EASA for the same flight.
etc.
Having 2 logbooks if you have 2 licences seems to be a good idea.
The techlog of the aircraft is another thing: it depends on the country of registration. To that respect I'm a little confused as it does not seem to be the same thing all over Europe. For instance if you fly a French registered aircraft, the rule is off block to on block on the techlog, just as the EASA rule for aircrews. In the UK it seems that only the actual airborne time is logged.
Part Q is still different. It's off block till on block or till the engines are out. I don't know if companies keep 2 sets of flight time logs for their pilots, part Q flight time and Aircrew flight time.