So, since I'm on a keyboard now:
Desktop power consumption generally isn't that good. The power supply ranges from 70-90% efficient (high efficiency power supplies are expensive, and only make a big difference if you're pulling north of 1000W), you've got external monitors that aren't usually built for incredible power efficiency, and you connect everything with decently long cables that take a non-trivial bit of power to drive. They're also generally built more for performance than power savings - higher power chips (that process faster), large hard drives, etc.
Laptops are literally optimized for power consumption. Battery life is everything anymore, and so they are hyper-focused on that. The chips are chosen for low power consumption, everything is tightly integrated, etc.
So, to save power, use a laptop.
Or, you can go with a desktop built out of laptop parts (or close to it). The Intel NUC systems are quite low on the power consumption scale, but you then have to consider the monitor power consumption (laptop screens are optimized for low power consumption, desktop screens typically aren't).
Now, why do you care? The best option in terms of saving money is to use your current machine (if it's only pulling 100W, it's not that absurd), sleep it when you're not using it, or power it down (both use little power). If you're paying $0.10/kwh, it costs you $0.10 to run your machine for 10 hours, so $7/mo for it being always on. You're not likely to be able to replace it with a comparable laptop for the expected cost savings.
If you're off grid and running on solar and battery, then the payoff looks better for dropping power consumption, but if you're grid tied, just put it to sleep aggressively and call it good.