That varies a bit depending on the system used: DogeCoin's authors, despite creating it as a spoof/joke, fixed a lot of the inherently wasteful processes and problems of the original Bitcoin. Thus proving that you have to do things better than the original for comedy, but I digress.
As a rough guide:
One (1) successfully completed DOGE transaction requires ~0.1kWh of energy.
This is about the same as running a gaming laptop for about an hour: it's also equivalent to the total end-to-end energy cost of 8 credit card transactions.
So, a fair amount, but not ludicrous.
Estimates vary as to how much a BTC transaction costs. According to Statista, it's now over 2,000 kWh - and this will only go up as Bitcoin's built-in artificial scarcity tightens. (Only 10% of the maximum BTC remain to be mined.)
Again, for comparison, that's roughly the amount electricity an average household of four would use in six months.
So,