GTA5 didn't run stable on last gen though, it could and often did drop hard when moving through detailed areas as the systems struggled to hustle data in and out of memory. And Assassin's Creed was a series notorious for uneven performance and characters popping in meters ahead of the player. Both were examples of the RAM limitations biting. It's not that last gen systems couldn't do open world, just that it was not their forte since of their three key components (CPU/GPU/RAM) the latter was the biggest bottleneck by far.
It depends on the platform and game. GTAIV ran poorly and still does on X1 BC. That's likely because its poorly optimized on CPU. GTAV was above average in performance, it stays pretty close to 30 fps while significant dips can be during driving and action. But that was par for the course on last gen.
In AC games you might see NPCs pop in fairly close, but they could also be seen from a great distances. You're exaggerating to make a point and ignore they were always raising the bar on visuals which is GPU heavy. These game also run better on 360 than you suggest, a lot of open world games performed better on 360. Many 360 games perform better on X1 BC because the bottleneck was on GPU. Meanwhile the game heavy on CPU still struggle. So Crysis 1 still runs bad while Far Cry 3 is a rock solid 30 fps.
Lastly, later 360 games actually required a HDD or USB memory sticks because external storage seemed to be used to give a memory boost, helped for streaming data quickly, etc. That suggest there was a bigger issue loading data quickly off a disc than just RAM limitations. Some games actually ran worse if you installed it on a HDD because it was using the HDD for cache, GTAIV was one of those games.
Gears 5 for X1X (5/5) - Mortal Kombat 11 for X1X (5/5) - Doom 64 for N64 (emulator) (3/5) - Crackdown 3 for X1S/X1X (4/5) - Infinity Blade III - for iPad 4 (3/5) - Infinity Blade II - for iPad 4 (4/5) - Infinity Blade - for iPad 4 (4/5) - Wolfenstein: The Old Blood for X1 (3/5) - Assassin's Creed: Origins for X1 (3/5) - Uncharted: Lost Legacy for PS4 (4/5) - EA UFC 3 for X1 (4/5) - Doom for X1 (4/5) - Titanfall 2 for X1 (4/5) - Super Mario 3D World for Wii U (4/5) - South Park: The Stick of Truth for X1 BC (4/5) - Call of Duty: WWII for X1 (4/5) -Wolfenstein II for X1 - (4/5) - Dead or Alive: Dimensions for 3DS (4/5) - Marvel vs Capcom: Infinite for X1 (3/5) - Halo Wars 2 for X1/PC (4/5) - Halo Wars: DE for X1 (4/5) - Tekken 7 for X1 (4/5) - Injustice 2 for X1 (4/5) - Yakuza 5 for PS3 (3/5) - Battlefield 1 (Campaign) for X1 (3/5) - Assassin's Creed: Syndicate for X1 (4/5) - Call of Duty: Infinite Warfare for X1 (4/5) - Call of Duty: MW Remastered for X1 (4/5) - Donkey Kong Country Returns for 3DS (4/5) - Forza Horizon 3 for X1 (5/5)