hps and mh

whats a more precise equation for growing, 1. 50 watts per square foot,or 2. a 5,000 lumens per square foot? I ask because i want to purchase a 600w grow setup, but it says that mh bulbs produces about 60,000 lumens, while the hps produces 90,000 lumens. If i follow the 50w per square foot i get a 12 foot area to work with both the mh and hps, but if i use the lumens ratio i get a 12 foot area for the mh, while the hps would get an 18 foot area. I want to keep optimal lighting for growth so which way should i go? do i need a more powerful mh than hps? I want to grow in a 4.5x4.5 room