My suspicion is the thicker bow may shoot faster but the thinner bow may last longer.
That is pretty accurate.
Limb thickness determines the strain/stress in the limb wood. The thicker it is the more stress the wood sees for any given amount of bend forced on it. Width determines the total draw weight because it determines the volume/mass of wood working.
The way I look at it is each piece of wood has a maximum stress level it can withstand before failing (typically by taking set in most hardwoods). This maximum stress determines the maximum thickness the limb can be for any particular bow design. At that maximum thickness every inch of width will develop a certain amount of draw weight. Width is then determined by what weight you want the bow to have.
Maximum efficiency for any given design is achieved when you take the wood right up to its stress limits, but not beyond. This equates to a thicker/narrower bow overall but if you go too far it will take set and lose performance.
Since wood is not predictably consistent in its properties like steel and other structural materials you either have to test and measure each piece individually or use experience and rules of thumb to guide how wide you make your bow and then refine it during tillering.
Mark