Ah ...... Mmmmm ....... Not exactly.
Ya' see, the load tables (as they are called in the tire industry) are set by Tire Standardizing Organizations. I talk about them here:
http://barrystiretech.com/tirestandardizingorgs.html
The load tables are the same regardless of who manufactures the tire. The quirk is that there are different tire standardizing organizations throughout the world and they have SLIGHTLY different answers to the question (Emphasis on the word" SLIGHLY!!"), so you have to be careful when comparing tires to understand which standard they are following.
44 psi vs 51 psi? That value is arbitrary: I talk about that here:
http://barrystiretech.com/loadtables.html
The load tables are the same for both (given the same tire standard)
Yes, It's complicated.
But for practical purposes, the load carrying capacity is the same at 40 psi regardless of what the max pressure is and which tire standard they are following. Put another way: The laws of physics decide how tires behave and the tire load charts are different ways of describing that.. And because the approaches are different, there will be SLIGHLY different answers, but the tire doesn't care. It's going to follow the laws of physics!
HOWEVER, there is a difference between SL (Standard Load) and XL (Extra Load) tires and they have different load carrying capacities - BUT - they have the same load carrying capacity at the same pressure. The quirk here is that SL tire's load carrying capacity maxes out at 35 psi, where an XL's maxes out at 41 psi.
So that addresses the first question.
The 2nd question? the 44 psi vs 51 psi shouldn't play into which you should be choosing.
And rolling resistance? For a given tire size, RR is a function of the deflection (mostly controlled by the inflation pressure), the amount of material in the tire (especially tread rubber), and the properties of that rubber.
There is a technological triangle for tread rubber compounds involving treadwear, traction (especially wet traction), and RR. To get better values for one, one or both of the others has to be sacrificed. That's why OE tires (the ones that come on new cars from the factory) have such a bad reputation. The car makers want tires with low RR (to be able to advertise better fuel economy) and they don't care much about how many miles the tires last before being worn out, and barely care about traction.
Roundness and footprint don't play much of a role in RR, except to say those impact how much rubber is used.