Overall, the two very different methods of transportation have surprisingly similar amounts of emissions, so close it's tempting to oversimplify things to a statement like "planes are 20% more efficient than cars". The exact circumstances make it so you can't say one is better in many or even most circumstances. Even worse, different definitions of "environmentally friendly" can produce estimates that vary by 50 to 100%. At the end of the day, for a two-person medium-range trip, a plane is slightly better for greenhouse gas emissions.
Expert Sources
The general question here about cars vs planes has been studied in great depth by experts, so I'll refer to them wherever I can. It's also a tricky matter where slightly different assumptions can lead to noticeably different outcomes. For example, BBC published a great article on the subject3 based on the UK's BEIS reports. The EPA also published a detailed report1 on vehicle efficiency that's regularly updated. I've reformatted a table from that report here and made the assumption that only two passengers are in the automobile.
The UK's Department for Business, Energy, and Industrial Strategy's 2019 GHG Conversion Factors for Company Reporting reports similar numbers but with a different methodology. These numbers do not include other emissions like contrails and soot, which can be according to the BEIS can be accounted for with a 1.9x multiplier for aviation.
Your question asked specifically about an A320. According to the the BEIS's report, an A320 is about average in load factors and emissions except for (rare) long-haul. So if you chose an A320 and not an A380, your long-haul numbers would be even better than suggested by the table above.
If, And's, and But's
There are lots of considerations here, like vehicle fuel efficiency, extra hotel visits, cargo, etc. However, we could just be getting nitpicky, so let's look at how big a factor those are. For example:
If you're in a car, your typical trip along some of the busiest airplane routes is about 1.08 to 1.27 times longer than a trip directly point-to-point (my own estimates)
An extra 50 lb. suitcase would require about 33 g CO2 per mile 1
An extra passenger in an automobile adds minimal extra emissions, but a lot of extra emissions on a plane
Cars produce several times more CH4 per passenger mile than airplanes do, and a little more N2O. But by my estimates this makes a small difference of less than 1%
Car emissions can vary a lot, with a 1984 SUV producing 8 times as much CH4 and 20 times as much N2O compared to a recent sedan.1.
Getting to and from the airport might take an extra 20-60 miles of travel each way
Staying in a hotel room (you're not really going to drive from San Diego to Portland in one day, right?) creates an extra 15.13 kg CO2 2
If we graph these considerations together we can compare their size. These are rough estimates and your exact emissions will vary.
Some of these considerations are huge, although some other considerations like staying in a hotel room or the trip to and from the airport are pretty minor. It makes little sense to say air travel is better for the environment without adding that many automobile trips are, in fact, better because there are 3+ people traveling or the trip is short.
It's an apples to oranges comparison
However, just comparing emissions per mile between the two is misleading. There are some big considerations like:
- Automotive traffic contributes to smog
- Many people go places by plane they would never go to by car
- Air travel often means you can't travel as freely at your destination
- When traveling by air you may have to drive something other than your favorite Tesla or Hummer at the destination
Contrails', soot, NOx, and other non-greenhouse-gas emissions effect on climate makes for a similar apples-to-oranges comparison. Contrails cause enough heating for their effect alone on global temperatures to be measurable. However, contrails also go away after just about a day, while CO2 emissions stay around for decades, some of it taking several millennia to dissipate. High altitude NOx similarly becomes less potent much faster than CO2.
Despite all these caveats, you can try to account for such emissions with something simple like BEIS's 1.9x multiplier, which the UK's BEIS says is often necessary, but admits that "there is no suitable climate metric to express the relationship between emissions and climate warming effects from aviation, but this is an active area of research. Nonetheless, it is clear that aviation imposes other effects on the climate which are greater than that implied from simply considering its CO2 emissions alone."
Sources:
1. "Emission Factors for Greenhouse Gas Inventories", EPA, last updated 9 March 2018
2. CHP in the Hotel and Casino
Market Sectors, EPA
3. Climate change: Should you fly, drive, or take the train?, 24 August 2019, Reality Check column
4. UK's Department for Business, Energy, and Industrial Strategy's 2019 GHG Conversion Factors for Company Reporting