I run the H600 currently. Very happy with it, I like the 18650 battery format. However if your trying to stay with the same batteries then of course the H51 is your light.
I know alot of guys really like the frosted lens, but I really feel for a all around lamp that is getting used out side having some amount of throw is very important. Say when you come to a clearing at night and need to see where the trail disappears off to. So I say the regular H600 over the H600f.
My brother has the H600w neutral white. It gives off a much warmer light color, closer to what a incadesecent does. Supposedly it offers better color rendetion? I dont know, the regular H600 doesnt bother me. It is a clean white, not blue. So go either way you want for that option.
Some guys complain that the H600 is too heavy and bounces on the factory headband. While I do agree that the headband is pathetic, simply rerouting the band to double through the rubber holder secures it down just fine. If they would have used a heavier elastic band in the first place than this would have been a nonissue.
Battery life is excellent and true to what is published. Ive used the H600 for several ALL night trips, as in I was on Med, low and High for 10hrs at a time. I use the 750lm High sparingly though. Ive also used it for ~12hr caving trips again with a variety of modes being used. I still carry an extra battery if I think Ill be using the light extensively. And I run good batteries in them, the AW 3100ah. Dont count on the cheap china batteries to be your only batt.
Get one, you shouldnt be disappointed.