I only have experience with tradidional EVA and a couple of TPU midsoles.
EVA in comparison generally often feels dead to me at toe off, whereas most TPU shoes i tried feel bouncier.
Never did timed trials to see wether I'm actually faster with them but feel wise i prefer TPU.
But midsoles can greatly vary even within a seemingly similar material. Both EVA and TPU can be super soft, but also hard as bricks depending on the mixture used.
Of course you can also have snappy toe offs with EVA foams, but these shoes then have in my experience way worse cushioning properties than TPU ones.