BA did a study a decade ago on glass systems. They concluded that SA was no higher with crew operating EFIS aircraft compared to crew operating conventional instruments.
That's probably because airliners had EFIS data presentation many years before they had anything one could call a moving map.
Another thing is that a typical airliner (especially one flying a typical
BA type of route) has little need for lateral SA because it spends most of its time at ~FL350 and is under tight radar control at the two ends. Anybody who flies IFR in CAS will know how this works. ATC keep you on a very short leash indeed.
This is why airline travel has historically been very safe (in the last few decades, anyway) despite the average 747 jockey knowing his lateral position to no better accuracy than a few miles, until established on the localiser
GA IFR is very different, with very different risks, and the pilot needs to be much more on the ball.