You might be considering buying stock in aircraft manufacturers such as Airbus (OTC;EADSY), or Boeing (NYSE.BA) right now. This assumes that commercial flights will return to 2019 levels by 2023. This is how industry leaders see things developing.This scenario suggests that new aircraft demand will increase, which in turn will lead to higher production rates and, ultimately, higher profits and margins.Which of the top two airplane manufacturers has the best recovery play? Let's have a closer look.Boeing vs. AirbusHistorical data shows that Boeing, at least prior to the 737 MAX disaster in 2019, generated significantly higher margins than its European counterpart and had significantly more free cash flow (FCF).This is something that could encourage investors to choose Boeing as a recovery investment. A recovering market for commercial aviation will result in more orders and production. Margins should increase as production grows, since airline manufacturers tend reduce their unit cost of production when they build more aircraft. This assumption is built into financial modeling. These are matters that Boeing has done better than Airbus in the past so it is possible that investors will favor Boeing.Valuations of Airbus and BoeingWall Street analysts believe that Boeing's earnings before interest taxation, amortization, depreciation and amortization (EBITDA), margin expectations will improve significantly. Below, you will see that analysts expect Boeing's margin to recover strongly by 2023.The consensus for Boeing is to generate $9.5billion in FCF by 2023, while Airbus will earn 5.1 billion euros. These numbers would place Boeing at 14.5 times the price of FCF in 2023 and Airbus at 16.3 times FCF. Both valuations are based on current market caps.These figures suggest that both stocks are attractive. These numbers suggest that both stocks are attractive. The positive narrative surrounding stocks will also change as airlines start to order again when commercial flights return. Southwest Airlines, for example, has ordered 134 Boeing 737 MAX planes this year. United Airlines, on the other hand, recently announced its largest ever order for 270 planes (200 Boeing 737 MAXs, 50 Airbus A321NEOs)It also looks like a better investment, considering that Boeing will trade at a lower FCF multiple in 2023 than Airbus.Case closed Boeing: It's not so easy.It is more risky to be a riskier personAirbus is a better choice than Boeing because there's more risk in Boeing's estimates. Although analyst estimates are good, they are dependent on the actual development of the businesses. Boeing has faced many challenges due to the COVID-19 pandemic.The first was that the 737 MAX grounded was an issue, but the COVID-19 pandemic shifted the market from a market for suppliers to a buyers market. Boeing might have to make pricing concessions in order to sell the 737 MAXs it needs to fill production slots.Second, Boeing's plans to build a new midsize plane (NMA), dubbed "797", have been delayed by the pandemic. This has allowed the Airbus A321XLR, a long-haul single aisle airplane, to take the lead in the market.The third is the expectation that domestic flights will be returned faster than long-haul international flights. This means that the narrow-body market will see a return sooner than the wider-body. Boeing is facing a problem because Boeing's management had previously placed its hopes on a wide body replacement cycle starting at the beginning of this decade driven by its new777X.Boeing or AirbusLooking into the future, Boeing's risk is that its revenue and profitability will fall short of expectations. This could be due to price concessions on the Boeing 737 MAX. Boeing may also find itself without an NMA. The 777X plane might not be as profitable in the long-term relative to expectations.These concerns do not necessarily mean that you should avoid Boeing stock. However, Airbus is the better option given the choices.