in my books, "sprinting" is anything 300m or less. Quarter-mile is pretty damn long to be sprinting all out.
Having said that, I think you buddy will beat you in anything less than 200m. Many BMX racers can generate very good anaerobic power, we're talking 1500-1800w. Your buddy may not be a true bmx racer, but he'll have good power, so I wouldn't under estimate him if it's 200m or less.