LONDON—Airbus SE vowed to use what it sees as its first-mover advantage to push ahead of arch rival Boeing Co. in the market for smaller passenger jets.

Boeing unveiled Thursday a deal to take control of Brazilian aircraft maker Embraer SA’s commercial aviation business. That follows Airbus’s own agreement, which closed on Sunday, to take over Bombardier Inc’s. CSeries jet program, which has pumped out a series of smaller airliners.

The...