Finance is about 7.3% of U.S. GDP [1]. The U.S. produces about 1,000 gigawatts of energy per year [2]. A first-order estimation thus yields 73 Gigawatts for finance. So about 150 times Bitcoin’s 500 megawatts.
About $700 million of BTC change hands every day [3]. That’s $250 billion a year. U.S. non-cash transaction volume is like $180 trillion a year [4]. So about 720 times the size of the Bitcoin economy.
Bitcoin thus appears about 5 times less efficient than the non-cash status quo. Given finance is less energy intensive than most of the U.S. economy, this is likely a lower-bound estimate.
[1] https://www.selectusa.gov/financial-services-industry-united...
[2] https://en.m.wikipedia.org/wiki/Electricity_sector_of_the_Un...
[3] https://www.quandl.com/data/BCHAIN/ETRVU-Bitcoin-Estimated-T...
[4] https://www.federalreserve.gov/newsevents/press/other/2016-p...