Air traffic for Ryanair grew by 13% while British Airways flew 2.6% fewer passengers during July when compared with July 2009.
Ryanair sold 7.61 million seats last month, smashing a previous record of 6.8 million seats sold in August 2009.
BA carried 3.19 million passengers last month, down from 3.21 million in July 2009.
BA enjoyed a strike-free July after cabin crew restarted talks about pay and conditions.
The long-running dispute has so far cost BA £150m ($240m).
Ryanair's figures came after a disappointing start to the second quarter when the Icelandic ash cloud had caused it to cancel almost 10,000 flights at a cost of 50m euros ($m; £m).
But in the 12 months leading to the end of July, the Irish carrier flew 70 million passengers.
"Ryanair's unbeatable formula of the lowest fares, no fuel surcharges and industry leading customer service continues to encourage passengers to switch from high fares, fuel surcharging [and] strike-ridden flag carriers," spokesman Stephen McNamara said.
BA said traffic should pick up in the months ahead.
"In winter we're likely to see more volume as capacity grows, but yield growth is likely to slow," said group treasurer George Stinnes.
Meanwhile, BA became the first UK airline to take delivery of the long range Boeing 777-300ER.
The state-of-the art aircraft is bigger, quieter and more fuel efficient than its predecessors and showcases the future face of British Airways.
In June, the European Union approved the planned merger between British Airways and Iberia without applying any conditions.