Once proof of stake is fully implemented and everything is migrated over, there will be no more energy intensive mining. Mining on a proof of stake chain just involves putting your Ether as a deposit that gets slashed if you act maliciously, the energy cost of this is just to run the servers, essentially, its you putting your money where your mouth is. Potentially, by the time proof of stake is fully released, the cost to run your own node (32 ETH) could be between 100-500k depending on the market value of Ether.
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.