Ryanair says it carried just under 3.77 million passengers in March, an increase of 26% on the same month last year.
But its load factor - the percentage of seats filled - dropped from 79% to 78%.
Meanwhile, British Airways says it carried more passengers last month than in March 2006.
A total of 2.79 million people travelled on BA's scheduled services in March 2007 - a 3.3% increase on March 2006.
The biggest increase was on African and Middle East routes where passenger numbers rose 9.4%.
BA flights were 76.3% full in March 2007 compared with 75.6% in March last year.
