The PTO generators I have seen need to run at a minimum RPM, usually a pretty high one.

So, as others have suggested, it depends on whether your load matches the generator, and whether the generator matches the engine that's driving it.

If you're running a much larger engine at a high RPM without needing the torque/horsepower it can provide, you're wasting fuel.

But there are other considerations -- larger, commercial-grade engines that are run and maintained regularly tend to be far more reliable than small, consumer-grade engines that are only run occasionally. And, despite potential fuel waste, the "care and feeding" of one engine is simpler and more efficient.

If you could put some sort of transmission between the PTO and generator, and find the sweet spot between RPM and torque, you would do much better fuel-wise. Wonder if that exists?