I don't agree with this. There is the theory and there are the facts. I think almost all the great looking Sony exclusives featuring good or very good amount of Anisotropic filtering proved us that this contention problem being the cause of low AF on many multiplatform games (but not all) was being blown out of proportion
You can't use some multiplatform games to judge a specific hardware problem. But if you take one of the best looking games this gen like: Infamous, bloodborne, Killzone and even a quickly done remaster TLOUR you realize they all have good or maximum AF applied while being graphically ones of the best.
Particularly the most impressive is Infamous SS IMO. Open world, high amount of polygons (>10 millions), high amount of high res assets and texture using very good amount (usually 8x) of anisotropic filtering applied. And that's almost a launch game so meaning the hardware is perfectly able of doing high AF and great graphics / performance with not much tweaking with the hardware and software.
I think they use low anisotropic filtering on many multiplatorm games because those games have to run on Xbox 1 hardware. Indeed this hardware showed us with some of its early exclusives (notably Halo5 and MCC) that it had serious trouble rendering decent amount of AF even when developed specifically for this hardware when 2 exclusives similar PS4 games (Killzone SF and TLOUR) were much better looking graphically while having a higher level of AF.
Overwatch had to run at 1080p on XB1 so they probably had to cut notably the AF (and use low resolution textures too) in order to do that (and the game still has trouble keeping its 1080p60fps target on XB1). But if you look at for instance The witcher 3 you realize this game has decent amount of AF applied on most textures (usually 4x or 8x and textures are higher quality) while being graphically one of the best looking multiplatform game with a very stable framerate. Well the game is running at only 900p on XB1...
My point being: yes the memory contention is a problem on all consoles but out of the box and just simply using the available tools, the PS4 is perfectly able to render great graphics + good framerate + decent level of texture filtering. Most exclusives and many multiplatform games showed us that it's a well balanced piece of hardware, well if you are using correctly all the cores of the CPU obviously.
Contention is going to hurt X1 too, like it hurt the Xbox 360 in some games and limited the original Xbox, I never said otherwise. In the X1 case Particularly when the backbuffer has to reside partially in ESRAM and partially in mainmemory. If Overwatch is deferred rendered with multiple rendertargets and given its 1080p on Xbox One it may be too large to fit in ESRAM and part of the render targets may have to reside in mainmemory. That would eat into main memory necessary for AF.
We've seen seen poor AF in some 3rd party X1 games when they have large 1080p render targets and are 60fps.
There are a couple of other things happening in Overwatch. Unlike Infamous SS/Bloodborne/TLOUR remastered it is 60fps, multiplayer, and its design mandates a solid 60fps above all else. A large overhead is maintained so when combat breaks out and a tornado of visual effects occur it still maintains the near rock solid 60fps. It is the Killer Instinct approach where that game generally runs at 90fps, but that performance overheard ensures the framerate never dips below 60fps no matter what. Unlike BF1 which can dip into the high twenties in multiplayer, and regularly dips into the 30s.