Most important differences:

100% Proof of Stake PIVX supports an advanced version of Proof of Stake (POS). This is a system that relies on master-nodes to verify transactions instead of miners. PIVX is 100% Proof of Stake whilst DASH is only 50%. This means DASH still relies on miners whilst PIVX does not.
Seesaw reward mechanism PIVX uses an advanced mechanism to distribute block rewards. 90% of the reward is distributed to the masternodes and stake nodes, whilst 10% is distributed to community projects.
Availability PIVX is a newer currency than DASH and less availability. It is traded on less trading platforms.
Speed PIVX is faster than DASH.

Important news for PIVX:

 

 
PIVX will become the first Proof of Stake (POS) cryptocurrency with zerocoin anonymous protocol. That means even more privacy than now!