Is that from Airbus marketing material? I really haven't noticed any big difference.
This article shows from an independent source shows the consumption is actually higher in the Airbus...
http://www.bizjournals.com/seattle/s....html?page=all
A 737-800 burns 4.88 gallons of fuel per seat per hour, compared with the comparable A320’s burn of 5.13 gallons per seat per hour, according to The Airline Monitor, an industry publication.