A lot has to do with the power to weight or the surplus power available to actually fly.
A lot of planes could not stay in the air one one engine, just how far they got from the engine failure varied. Some planes had a negative climb rate on one engine. (Saro Lerwick, certain versions of the Whitley with lots of antennas, some Wellingtons were suspect.
A P-38 can fly on a lot less than 1000hp from one engine.
DC-3 can fly on one engine, early ones had only about 1000hp per engine or a bit less.
The Problem with the JU 52 is it needs a fair amount of power just to cruise at 130-150mph.
the DC-3 (in one version) could cruise at 205mph using 75% from both engines. Engines were rated at 1050hp at 7500ft max continuous so 75% was 75% of that, not take-off power.
Max speed (using 2550rpm/100% ) was 230mph. Stalling speed with flaps and gear down was 67mph. The DC-3 had a lot of room if an engine went out. This was at 25,500lbs (later ones got heavier)
The Ju 52 bludgeoned it's way through the air. It needed about the same amount of power to go 140mph (give or take) as the DC-3 did to go just under 210mph.
We know the cube root rule. The JU-52 and a number of other tri motors used the 2/3rds power to stay airborne.
Some planes were better than others. The Lerwick wouldn't even fly straight but descended in circles until it was reunited with the surface.
This is one reason for the canted engines on the Ju-52. It was supposed to make it easier to fly if the off side engine went out.
edit.
Info from the 1938 Jane's
Performance is a bit higher than Wiki, commercial plane, no gun mounts/turrets.
Top speed 180mph at 3,000ft.
Gross weight 23,200lbs
Climb to 1000 meters 4.8 minutes
Climb to 2000 meters 10.2 minutes
Climb to 3000 meters 17.5 minutes
Service ceiling 5,500 meters (19,020ft)
Ceiling with one engine stopped and weight of 20,900lbs......3,300 meters(10,824ft)