Phenomenal question. Did you know you're my second favorite user on this forum?
Anyway that answer is that it depends on the exact PSU, and the real answer goes in contrast to what popular belief is. So here is what popular belief is:
If you have a computer with, say for exemplary purposes, 425W of load when gaming, and you have two power supplies: a 450W and and 750W, both based off the same platform (this is important, since they are similar), the 750W power supply will last longer. What would be the general reasons to support this? Intuition says:
-) It has "more beefy components". What does this mean? Well, higher wattage units have higher rated bridge rectifiers, rectifiers, switching transistors, and transformers. This argument can fall short, though, because frankly these are lesser likely to fail compared to other components of the power supply like capacitors and the fan.
-) It is more efficient at 425W load compared to the 450W PSU. This means less waste heat. This is true and probably the most important factor for why such a unit, if it does, would last longer compared to its 450W counterpart.
Now here is the real response:
If you have a computer with, say for exemplary purposes, 425W of load when gaming, and you have two power supplies: a 450W and and 750W, both based off the same platform (this is important, since they are similar), it cannot be determined which will last longer. What would be the general reasons to support this?
-) Fan profile. While the 750W unit will have less waste heat, its fan might be spinning slower than that of the 450W unit since its bridge rectifiers, switchers, transformers, etc. can take more heat. But you know what the slower-spinning fan does harm? Capacitors. Heat hurts capacitors. So while a 750W unit has less waste heat, the 450W unit's fan may actually be exhausting more heat and leaving the capacitors cooler.
-) Specifics of the design, too far for any of us or a reviewer to really understand fully. Power supplies are really complex, designed in large groups. It's hard to just make assumptions, even if it seems natural.
Now here is the reality:
In most cases, yeah, probably the 750W unit will last longer (but we can't be sure, the 450W unit might last longer). But the thing is, the 750W unit probably costs 50% more than the 450W unit. Now here is the question. Will that 750W unit last more than 50% the life of the 450W unit? I reckon not. I doubt it. I think money is better invested into an even better 450W unit in this case. If I can choose between a very good 750W unit or a phenomenal 450W unit for the same price, I would choose the 450W unit. This is because part of the money that goes into the 750W unit is for things that your computer won't make use of - a larger bulk capacitor for better holdup times, higher rated rectifiers, switchers, etc. Whereas the "phenomenal 450W unit" will have money put into stuff that will probably benefit you more, which could be a whole variety of things.
I think buying the higher wattage unit is silly because it is accommodating for something where money was even spent for that won't be made into use. It's like making a train meant for carrying a few people with 100 seats. Whereas, you can build a golden train with TVs in front of the toilets and accommodate 10 people. In the end, the latter is the better train. This is why I always believe in sort of living on the brink a little with power supplies - but to accommodate for that higher load percentage by just getting a really good power supply, which does not have anything to do with that wattage number on the label.
And I feel like I just conveyed literally everything that's been on my mind for weeks into the perfect words. This was good.