ICAO Annex 6 Part 1, Attachment D-1 paras 2.2.2 and 2.3.1 are worthwhile reviewing in this conversation.
There is a difference between the conditions for a 2 engine or a more than 2 engine case. It can often be the situation that the 3/4 engine aircraft depressurized is actually using less fuel than all engine case depressed. In 2 engine case, almost always you are better off on one as far as fuel goes, not so great on your cardiac system though.
I'm only familiar with some NAA regulatory reqts, so season to taste, but of the dozen or so different rules that I have operated and continue to operate ETOPS/EDTO/LROPS, there is a difference per Annex 6. If your NAA has something different, then that is great, they only have to notify ICAO within 6 months of variations to ICAO standards.
My current rides will either end up better off on one engine depressed or will end up with a dive over the side. In either case, fuel is not a big worry at that point.
just checked the OPM on a couple of the different jet types I fly, and both of those show that the SAR improves for the 2 engine jet, with an engine shutdown, at low altitude, which is also what was the situation in the last 4 engine plane I drove, and the last 3 engine jet as well. (results may vary, seek medical advice if... etc)