ATR Both Engine FlameOut Checklist
 

5 Years on I think to myself Why does the Both Engine Checklist tries to recover Eng2 before Eng1 despite the Left being the Critical....

I assume "Because the checklist Says so" ...

You may find the choice is determined by the aircraft systems.

One of the nice things about the ATR, is it doesn't matter which engine comes on line. As long as one engine is started (and both DC and AC gens online), all systems will be powered. Hydraulic pumps are electrical, so no EDP to worry about. Another nice thing about the ATR, is it has a tendency to go straight irrespective of which engine is lost. The "critical engine factor" is negligible. My assumption for the checklist being written that way is because that's the sequence the engines are started on the ground. Just to standardize things. If there's another reason, I'd love to know!

maybe the batteries are closer to the right side and less length of wires for better/quicker start?