from the pic, the new device seems ponderous, and relies on separate refrigerant than the liquified H or O. Quite a bit of extra weight.
My understanding is that the liquid nitrogen is just for the ground tests of the heat exchanger. An actual engine would use the liquid hydrogen fuel for this purpose.
Edit: I think you're talking about a picture like this one:
There is indeed a separate helium circuit to transfer heat in two stages rather than just one. I thought you were referring the the ground tests where they are using liquid nitrogen in place of liquid hydrogen fuel.
Still, if the weight of the heat exchanger is less than the liquid oxygen you'd have needed to carry, it's still a win. For a conventional rocket to do single-stage to orbit, you'd need around 89% of the take-off mass to be fuel:
Tsiolkovsky rocket equation - Wikipedia, the free encyclopedia
Only 11% can be engines, tanks, structure, payload, re-entry heat shield, etc.
For a two-stage to orbit rocket, the number becomes 84%, which is a bit more manageable. Of this, 67% of the launch mass is first stage fuel. Oxygen has an atomic weight of around 16, so you have 8 times as much mass of oxygen as hydrogen. So about 58% of your launch mass is liquid oxygen for the first stage. If you can air-breath for the time the first stage would normally fire for, you can save most of this mass (but you have to add on the weight of the heat exchanger and the extra hydrogen tanks you now take to orbit). Still, it's not hard to see why this might be a big net win.
What the diagram doesn't show is what happens to the nitrogen from the air. Presumably this has to go though the engine too. Wonder what that does to the combustion chamber design - having nitrogen in the mix for the first half of the burn and not for the second?