Now, assuming every single one of the 110,000+ validators runs on a dedicated machine (which is not the case) and consumes 10 W * 24 h = 0.24 kWh of energy daily, we get an annual energy consumption of roughly 87.6 kWh per validator.
Extending this assumption to the 110,000 validators currently validating on the mainnet, the annual energy consumption of the network would be 9,636 MWh, or roughly 10 GWh annually. In reality, this value is close to a worst-case scenario, as running multiple validators on one machine doesn't affect the load of the machine in any meaningful way. One could run 1000 validators on one Intel-based NUC.
For reference, the current PoW Eth chain consumes roughly 40 TWh of energy annually.[1] Assuming the annual energy consumption of 10 GWh for the PoS chain, the energy usage would drop by 99.975% (three orders of magnitude; E12 -> E9).
Assuming an error of an order of magnitude in the calculations for the PoS chain's energy usage (which would mean running every validator on a dedicated PC pulling a continuous 100 watts, or alternatively 1,100,000 validators), we'd still drop the energy usage by 99.75%.
The benefit of this with the mining algorithm that Ethereum uses is that you can mine with off the shelf consumer parts. When proof of stake is fully switched to, those parts will just be sold on the market.
With Bitcoin, switching over to something like proof of stake will be extremely political and will only work out if the market decides that the new proof of stake blockchain fork is the 'real' Bitcoin. It will be political because miner's mining hardware becomes e-waste so they have an incentive to continue mining regardless of the fork. The only way that miners stop mining Bitcoin is if the blockchain becomes worthless in the market so that the miners no longer can afford to pay their operating costs with the mining rewards.