On a lot of twin jets, the critical engine (= the one that's going to effect your systems the most) will be No. 2. The reason is that the Captain's systems (Comms, Nav etc) are on Essential Bus but the Co-pilot's are on plain No. 2 Main - any engine problems & you're likely to lose ILS & Autopilot just when you don't want it.
More modern twin with solid state switching don't have a problem but on the older/less sophisticated models it can ruin your approach.