I think there's a lot of different things going on here. I will try to address each of them in turn.
First of all, it has been my experience that you are doing yourself a great disservice by trying to use a head lamp not in total darkness. I don't know if you are, but you said you go running before sun up so I assume it gets light at some point during your run. I have always found that a little bit of daylight (even a VERY little bit) makes my lights appear to perform very differently. I prefer to run in either total darkness where my lights perform very well, or in enough daylight that I don't need a light. When I do get caught doing an adventure race that spans day and night, I always find dawn and twilight the hardest times to regulate my light situation. I'm just throwing this out there because it's something I've noticed although I really don't have an explanation (or a solution).
Second: You're not comparing apples to apples. You asked about lights that have the "same amount of lumens & a similar beam profile" but they do not have the same beam profile. The H51w and the SC60 have the same emitter but the SC60 has a larger reflector. This will always result in a tighter beam, and the perception of increased brightness. I'm not saying this is the whole reason for what you are experiencing (as you will see below) but I believe it could be part of it.
Now, if we do compare apples to apples (I have both the H51 and H51w) The H51 does seem noticeably brighter, even when on comparable levels. But again, I believe there are some faulty perceptions that may cause us to think that the H51 is better at lighting up the trail. Let me explain:
When you're running on a trail, you're looking primarily at objects that are various shades of browns and greens. When you shine a cool light in front of you, the contrast between the areas that are illuminated by your light and those that are not is greater than the contrast would be with a warmer tinted light. This creates the perception that the light is brighter. In fact, you don't actually want a bunch of cool light reflected back to your eye. You want the color of whatever the object is that you are illuminating to be reflected back to your eye. The problem is that when this happens, you don't notice as dramatic an increase in contrast between light and dark as you do with a cool light so your brain thinks that you're not seeing as much light. You see, you brain knows what color it expects things to be, so when it sees them appear in those colors, there's nothing surprising. But when something appears with a bluish tint caused by a cool light reflecting off of it, your brain immediately recognizes that something is different from normal and that difference registers a larger magnitude. Sorry if this is a poor explanation but it's the best I can do.
Now I'll talk about something else I've noticed regarding the H 5x series lights and trail running. The beam pattern of the H51/H51w is actually a little too tight for trail running. The problem is that I naturally adjust the hot spot such that it is right in the middle of my vision, where I'm looking most of the time. I imagine this is what most people do. What I noticed though is that because I'm staring right at the hot spot, my pupils tend to contract because there is a ton of light bouncing back in from one place, similar to looking at the Sun. When you pupils are contracted like this, your eyes tend to shut out what is being illuminated by the spill in your periphery. It's kind of like when people use video cameras to do beam shots of lights. When they first turn the light on, the sensor reacts by limiting the amount of light it lets in because the hot spot is so bright so all you see on your screen is a round circle of light in the middle when you know very well that there are several lumens of spill. To test this theory, I put some commonly used diffuser film (dc-fix) on my headlamps. I expected that the perceived brightness of the hot spot to drop because the hot spot was diffused but what I discovered was actually the opposite. Because there was no super bright hot spot, my eyes did not try to adjust as much, and everything appeared brighter. There was no noticeable loss of brightness in the center of my vision but everything in my periphery became brighter. I could now see the entire width of the trail illuminated evenly and my eye was more aware of what was happening at my feet, out in front of the hot spot, and on either side of the trail. I did one light first and took both out on the trail. I ran with both for part of the run but I quickly became annoyed with the un-modified light because I felt like I had tunnel vision. I ended up completing the run with the diffused light on my head and the other in my pocket. When I got home, the first thing I did was cut out another piece of dc-fix and stick it on my other Zebra.
The long and short of it is, there are probably several things contributing to the perception that the cool light is better at lighting up the trail. I think if you look critically however, you can see why some of those might be misconceptions. Also, try some diffuser film. I know you're hesitant to lose some throw, but in practice it makes the whole experience more enjoyable.