There's confusion here. Where can I find a reference to those claims about major differences between li-poly and li-ion? As far as I know, they are for all practical purposes very similar. And li-ion is absolutely as dangerous as li-poly when punctured.

The major difference is really that li-polymer batteries are soft (if delivered without an extra, external hard case) and can thus be shaped to some extent. I replaced the li-ion battery in my Palm with a larger capacity li-poly, as the latter could be shaped a little it was possible to put in a battery with 40% larger capacity. And yeah, it's about 40% larger by volume too.