You answered your own question. The Lime build includes extra hardware support and removes the requirement for PAE. The site you linked to displays a list of hardware that it adds support for, so if you have one of those, then you should get Lime, otherwise Vanilla should suffice.
PAE lets 32-bit processors to access more than 4GB of RAM. Vanilla requires PAE to function which limits it to devices that support that, but Lime doesn't force it, so you can use it on more devices.
Lime is best for newer systems that have hardware that Vanilla does not yet support (or even know about). Plus, Lime gets updated more frequently because if you have hardware that it doesn't support, you can contact Hexxeh to have him add support.
If your processor does not support PAE, then you must use Lime since Vanilla won't work on it. If your system does have PAE, but the hardware is somewhat old, then Vanilla will likely work.
Essentially, Lime is cutting-edge (i.e., beta) while Vanilla is the stable release. Frankly, you may as well use Lime in general unless you don't want to/may not use beta software and want/have to use a stable build.