One principle of skating is that the faster a skier's velocity, the more acute the V of the skis can be. Meanwhile, the slower the velocity, the larger the angle will be. We can see that for ourselves: When we V2 fast, the angle of the skis may be around 30˚; and when we're casually skiing uphill, the V expands to 90˚ or more. There are some laws of physics at play here, but in general, we figure this concept out ourselves - it's really hard to skate up a steep hill with a tight V.
Another concept is not exclusive to skiing: The quicker you try to do something repeatedly, the less time you have between efforts. That is, if you're skiing 40 strokes per minute, you have 1.5 seconds to move from ski to ski, and if you're skiing at 90 strokes per minute, you only have 0.66 seconds to shift your weight.
As you mention, "it seems like the new skate only works at high tempos or going uphill," and I basically agree with that. When the tempo is high, you may not have enough time to shift completely over to each ski (into the "old" toe-knee-nose) - especially if you're going uphill using V1/offset, with a wider V. It's also a safe bet (hope?) that your high tempo is also making your ski speed faster, so the V in V2/one-skate is more narrow; you may actually be getting completely over each ski, but it's a less obvious weight shift.
I'm not sure why there are "new" and "old" skates being taught, as both are valid. There's a continuum of how much weight shift and torso alignment you can effectively achieve in different conditions, and you need to figure out what works best for you. Ski speed and the terrain contribute to making this decision, but so does your strength and balance. If you look at this video, we can see that Sundby (leading, red bib) is able to stay squared up to his skis more effectively than Sveen (bib 17), who is using more of a toe-knee-nose approach - but they're skiing at the same velocity...
-Jason Cork
US XC Ski Team Coach
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