I would love to see some analysis somewhere about the comparison of energy usage or carbon output of everyone recharging mobile devices vs. using (recyclable!) paper boarding passes.
With screen on full brightness and CPU running at full blast, 500mA @ 3.7V isn't an unreasonable upper bound estimate of power consumption for a typical mobile phone. Assume you spend 5 minutes checking in and acquiring your boarding pass, 2 minutes looking at it as you head to the gate, and 5 minutes displaying it to board: a mobile boarding pass use likely consumes at most 0.37Wh of energy. Assume 80% efficiency in the charger and another 80% efficiency in the battery circuitry to get a 0.57 Wh total consumption. At the US average of
0.947 lbs CO2e per kWh, you're looking at 0.00054 lbs of CO2, or roughly 240 milligrams.
The carbon emission of plain paper production, factoring in recycling, is 4.25 kg of CO2 per 500 sheets of paper, so about 8,500 milligrams of carbon emission for a piece of paper. And that's
before you pay for the electricity to run the printer and desktop computer that's printing it; a typical laser printer draws 300-500 watts while in operation.
Direct thermal boarding passes printed at the airport are a bit more complicated to analyze: those printers tend to draw 15-20W while in use, so they're a little more power thrifty... although still in a completely different league from your phone. The paper is more toxic to manufacture, though, due to the coatings on the paper that produce the thermal printing effect (historically, BPA, although alternatives are now in use); many recycling facilities actually will not accept thermal paper as a result, so boarding passes may not be recyclable in many municipalities. And you still have to account for the 150-300W the kiosk is probably using.
tl;dr mobile boarding pass is
much more environmentally friendly, if that's a priority.