Your neighbor may have a different type of grass growing in his yard and they all grow at different rates.
How come Whenever I mow my lawn the short grass grows faster than my neighbor does. Doe he put something special on the grass to keep it longer. I have to mow it more often?
Different type of grass or maybe a sunlight and drainage difference.
Everything being equal (as in type of grass, soil, etc) the height you cut your grass down to can effect growth.
