FARNBOROUGH, England — Boeing beat Airbus in the aircraft order stakes at this year’s Farnborough Airshow, booking potential deals worth more than double the size of its European archrival.

Though the highlight of its week was unveiled Thursday in Chicago, where Boeing announced a United Airlines order for 150 aircraft, Boeing said it took total orders and commitments over the past week for 396 airplanes, valued at around $37 billion.

That is more than double Airbus’ performance of $16.9 billion in orders and commitments for a total of 115 aircraft.

Boeing left Farnborough in better shape than a year ago, when Airbus scored big in Paris — the French capital and Farnborough take turns hosting one of the aviation industry’s prestige events — with a series of deals for its revised short-haul aircraft, the A320neo.

Neither company will reap the full list value of its announcements, as customers rarely pay the price when ordering big. And though most commitments end up becoming firm, it’s not unknown for them to fall through at the last hurdle or two.

Even so, the past week provides some relief for Boeing, though it still has a long way to go to make up for last year’s shortfall, when Airbus clinched $72 billion worth of orders, around $50 billion more than Boeing had secured.

Most of Boeing’s business this week has been to respond to the challenge presented by the A320neo. Its 737 airplane, particularly the new MAX version, did well, especially when the company agreed to a $14.7 billion firm order with United Airlines.

After inspecting what was available, including Airbus’ A320neo, United, the largest U.S. carrier by revenue, agreed to buy 150 Boeing 737s to replace older planes that are not as fuel-efficient.

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United’s order includes 100 of Boeing’s new fuel-efficient 737 Max 9s, which will start being delivered to United in 2018. United also is buying 50 of Boeing’s current 737s, which are due to start arriving in late 2013.

Despite the order from United, the airshow’s business has been cooler this year.

Boeing’s stream of orders with leasing companies such as GE Capital Aviation Services and Air Lease Corp. failed to excite, while Airbus mustered only one airline order, albeit a strong commitment from Hong Kong-based Cathay Pacific for its new A350 long-haul aircraft.

The decline in overall orders is no surprise given the gloomy global economic backdrop and the scale of government cutbacks around the world.