They lose just about everything.
From the SRD:
The creature loses the natural weapons, natural armor, and movement modes of its original form.
Pretty much makes Warforged pointless as druids.
None of these matter, because chances are that your new form will have better stuff anyway. Natural weapons don't matter because the WF has exactly one: Its slam, and that deals 1d4 damage. NA doesn't matter because the Warforged only has its inherent armor bonus, and that's +2, +3 if you took Ironwood Body, or +0 if you took Unarmored body. Movement modes don't matter because the Warforged's are average. The things that do matter are the Living Construct subtype, which grants a lot of immunities and other neat stuff, and the Con bonus. The former you keep. The latter you lose, but the bonus hp you got stays.
Honestly, the big problem with Warforged is that they take a hit to Wis, not what they lose when they Wild Shape.