I'm just starting out with Pd, and want to know what factors I consider in choosing between using Pd vanilla vs. Pd-extended.
For beginners Pd-extended offers many convenient tools and comes with many externals, abstractions and GUI-plugins already pre-installed (and direct access to the bug tracker) that you might find useful to get started. However you can still have Vanilla Pd installed alongside and try Pd in all flavours. Vanilla is usually a little more up-to-date and has the freshest improvements, because it takes time to be packaged in a Pd-extended (at the time of writing this, Extended is at 0.43.4, while vanilla is at 0.45.4.) Under some circumstances, like when you develop for libpd or for the Raspberry Pi, you might be limited to the vanilla set of objects. Testing your patch against vanilla and knowing it's dependencies on abstractions or externals is considered good practice, then you can decide whether to get rid of the dependencies, include the abstractions with your patch for distribution or assume Pd-extended and declare the dependencies properly (by using an object [declare -lib {name of lib}]). Purists who restrict themselves on vanilla on the other hand, might call Pd-extended "bloated"; but then we are getting into matters of taste, style and personal preference.
Update 2016: By now the situation has changed somewhat. Pd-extended is abandoned and will not be updated any more. It is still available and features some redesigned and organized helpfiles amongst other things. However, vanilla is the current Pd and through the deken plugin, there is a convenient method of installing libraries which you might be missing.
Update 2018: Pd-extended is now deprecated and left far behind the current features of vanilla Pd. There is no more reason why one would use Pd-extended and it should be discouraged to do so, new users should not begin with Pd with a dead-end branch. A new offshoot is Purr-Data which tries to take on where Pd-extended has left off.