European manufacturer Airbus managed to steal a march on its American rival before the show - at Le Bourget just north of Paris - with a successful maiden flight of its new A350 long-haul plane.
Airbus is pinning its hopes on the fuel-efficient A350 to compete in the long-haul sector after gradually winning more than half of the market for medium-haul, single-aisle planes that carry an average of 150 passengers.
The A350 is expected to conduct a fly-by of the air show towards the end of the week, hoping to woo potential customers.
During the show, famous for high-profile announcements of big-money deals, Airbus hopes to add a slew of orders for the plane - set for delivery at the end of 2014 - to confirmed contracts with Qatar Airways, British Airways and Hong Kong's Cathay Pacific.
Nevertheless, Boeing is also entering the show in bullish mood as it seeks to move on from its difficulties with the trouble-prone 787 Dreamliner.
Technical problems with overheating batteries forced the worldwide grounding of the Dreamliner fleet in a major setback for the Seattle-based manufacturer.
Boeing will showcase the Dreamliner at the event and the firm is expected to announce the launch of its 787-10X, a longer version of the original Dreamliner, which can accommodate up to 330 passengers.
The US firm is also set to announce in the coming months an up-to-date version of its existing 777, with wings made of fuel-saving composite material like the Dreamliner.
Boeing boss Ray Conner said it was going to be a "great competition" and said that airlines would "benefit from the fact that both companies are going to have a good wide-body product line."
"I think we have the better products and at the end of the day, hopefully the better product wins," Conner told reporters on Sunday.
Airbus has positioned the A350 for the market between the popular 777 and the 787, hoping to steal share away from both planes.
The European firm argues that its craft will consume six percent less fuel than the 787 and a quarter less than the 777.
Boeing's strategy, on the other hand, is to offer its clients a wider choice of long-haul airliners but Tom Enders, boss of Airbus parent company EADS, said "the jury was still out" in terms of the firms' respective market situation.
"It's premature to draw any conclusion and it's not necessarily the one who has more products who is also better positioned on the market," said Enders.
And analysts warned that Boeing's recent technical troubles may yet haunt the US firm.
"Airbus can, and will, argue that Boeing's ability to execute is questionable and that the A350 is a better bet in terms of timing and availability," said Richard Aboulafia, a US-based aviation expert.
But the Paris air show, in its 50th edition this year, is not just about commercial battles and the long-awaited A400M military transport plane will also likely provide a highlight as it takes to the skies.
The market in unmanned surveillance drones will also be in focus after three top European defence companies urged the creation of a European programme to manufacture the craft, currently available only from Israel or the United States.
The Paris Air Show runs from June 17 to 23. It is expected to welcome some 350,000 visitors through its cavernous show halls.
The event, which has become the global aviation industry's largest in terms of surface and number of exhibitors, will throw open its doors to the public on June 21 after first welcoming professionals.