There's no such thing as a straight port. The assets are moved over, but the engine that actually runs the game and handles the assets is different between the two platforms. There is probably a ton of common code between the two engines, but the underlying architecture, particularly graphics capabilities, is so different that they have to have significant code changes to make the game run well on either platform.
It's that engine that decides when to load something, and where to hold it for when its needed, and that appears to be the crux of your question.
However, it's mitigated by the asset pipeline. Most pc games run from the hard drive, which is fantastically faster than the optical drive in any console. Even if a game is forced to run in a 32 bit address space, it can load man more things on demand from the hard drive that would take too much time on the console.
If anything, I would say the console is more restrictive in terms of raw data handling capacity and capability, for handling physics, ai, etc in a timely manner.
But again, this is all handled by the engine, and in a multiplatform game, the engines are different enough between the platforms that the 32 bit or 64 bit distinction hardly matters.
You could think of the engine, in fact, as a virtual machine. It's upper interface to the game is the same across all platforms, and the lower interface takes as much advantage of the underlying architecture and resources as possible, and runs the game as well as it can given the resources available.
This suggests that 1) the engine for the pc is far more complicated than the console engine because it has to adapt to different resources and 2) that the pc platform could be both better or worse than the console based solely on the engine design and adaptability and the underlying hardware. I'd fully expect to see much better graphics on a pc setup for the same game on a retina display with a high end GPU, and much worse graphics for a very low end graphics card, compare to a console version.
As far as ai and physics, they are minuscule compared to the graphics processing, so I don't expect you'd see much difference unless they made the engine different intentionally. I'd expect them to do this if they recognize that pc gamers have a different play style and set of preferences than console gamers, but otherwise I don't think it would come down to resource constraints.