Some heavies (747, 777, A380) fly short- to medium-haul in Asia and the Middle East. You could say they're stealing jobs from 737's and A320's.
Anyway, what I could find was for the US only.
Checking the Revenue Passenger Miles Total by Aircraft Type for 2016 on transtats.bts.gov we find—
- All 737 variants: 153.2 billion
- All 777 variants: 38.3 billion
Expanded:
Boeing 737-100/200 18,374,213
Boeing 737-200C 58,536
Boeing 737-300 6,609,070,471
Boeing 737-300LR 574,860
Boeing 737-400 1,484,593,783
Boeing 737-500 324,819,083
Boeing 737-700 44,485,736,725
Boeing 737-800 69,014,076,197
Boeing 737-900 18,203,949,655
Boeing 737-900ER 13,058,102,746
Boeing 777-200- 32,808,990,997
Boeing 777-300- 5,466,846,693
Top types with at least 10 billion pax miles:
Boeing 737-800 69,014,076,197
Airbus Industrie A320-100/200 48,907,277,978
Boeing 737-700/700LR 44,485,736,725
Boeing 777-200ER/200LR/233LR 32,808,990,997
Airbus Industrie A321 28,492,821,887
Boeing 757-200 26,182,350,221
Boeing 767-300/300ER 24,176,619,545
Airbus Industrie A319 22,087,734,671
Boeing 737-900 18,203,949,655
DC9 Super 80/MD81/82/83/88 15,379,739,818
Boeing 737-900ER 13,058,102,746
Airbus Industrie A330-200 10,556,831,804
From this top list:
- Single-aisle: 285.8 billion
- Widebody: 67.5 billion
(Narrow- vs. widebody above is just in case you are wondering. Arbitrarily selecting top-x won't reveal much.)
Boeing's outlook for the future based on past- and current-trends sees the single-aisle market outgrowing the widebody.


I've tried to dig deeper, but it seems some 260 governments don't openly share those statistics, we'd need to hire an analyst firm for a worldwide view.