The TP2 says "Li-ion" whereas the DI says "Li-ion Polymer". I was under the impression that most cell phone batteries are polymer since they started exploding (as well as many laptop cells).
LiPoly lasts much longer in terms of service life and is much easier to get higher energy density for amount of space used. They're possibly more dangerous than standard LION though.
Since there aren't that many sources to get LiPoly, I would imagine they're a higher quality than LION which has a much wider gamut of sources.