I could be reading the tooltips wrong but they seem to do the same thing except like you said, NF works on allies. Why not just make it 1 button and work on allies or self? Both provide 10% dmg reduction, life leech on weaponskills and a barrier.
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Nascent Flash heals both the user and the target, whereas Bloodwhetting only affects the user.
So, in scenarios where both tanks are taking damage (like the first two phases of TEA, for example), the most powerful option would be to have the WAR use Nascent Flash and the other tank use targeted TBN, targeted HoC, or Intervention (however, Holy Sheltron is superior to baseline Intervention, so you may still just use Bloodwhetting with a PLD co-tank).
The WAR only gets Nascent Flash; they don't receive Nascent Glint (assumedly, they similarly don't receive Stem the Tide nor Stem the Flow). So, unlike in Shadowbringers, there will be no reason to use Nascent Flash solely for personal use in Endwalker.
There probably is a way to consolidate Nascent Flash and Bloodwhetting into one button without nerfing or buffing either ability, but it would be fairly convoluted. For instance, it might be possible to separate Nascent Glint into two different effects but disallow the stacking of the two healing effects. However, that's a bit inelegant, and it would make Nascent Flash apply yet another effect (which can be problematic if buff limits are a concern).