the Airbus family of aircraft cruise at a significantly lower Mach Number. I'm guessing at around .76 (someone will correct me I'm sure)
Prepare to be corrected! The Airbus "family" is huge and varies from the A318 to the A380. At normal cruise altitudes, the A320/A321 will cruise at about M.78 whilst the A380 will be somewhere towards M.85.
The assumption that Boeings are faster than Airbuses simply isn't true and is a huge generalisation. The B737-200 for example flies (flew) at M.72, the 737-300 IIRC is M.75, both slower than airbus narrow body aircraft which in turn are slower than most widebody aircraft.
It's all about fuel these days not racing around trying to shave 2 minutes off a flight!