The EOS 2 and the new EOS are a little brighter on high than the Quad. These are the approximate lumen ratings for each setting.
EOS: High-50 lumens, Medium-20 lumens, Low-5 lumens
EOS II: High-50 lumens, Low-10 lumens
Quad: High-45 lumens, Medium-20-25 lumens, Low-10-12 lumens
The EOS headlights are brighter and have better runtimes on high. The Quad is the more efficient one on low. On medium, they are comparable in brightness and both have about 10 hours regulated. The EOS and EOS II now have the more even beam pattern. The Quad's l.e.d.s have been angled toward each other to make one spot for more throw. The Quad still has massive flood light, but more of the light has been concentrated into the spot. The EOS has a good balance of spot and flood that lights up as a square covering an entire trail with light but the spill light doesn't extend to all of your peripheral vision. The EOS has the best range of brightness settings. The EOS has the highest high and the lowest low which will give you the best runtimes of the three lights on both high and low. The EOS II has a simpler U.I., has a higher safety rating, and comes with a rubber strap and stick on velcro for hard hat use. The Quad has about the highest low that is more efficient. At that brightness level, it should last longer than the EOS II low and is probably still bright enough for hiking with night adapted eyes. The EOS headlights have a more even beam. The Quad has a large spot beam and massive, dimmer spill light.