Nature of Connection:
Dataset: is generally used to employ disconnected architecture of Ado.Net
DataReader: is directly connected to database system with Forwardonly cursor

Local Storage:
Dataset: It reads data from database and stores in local system.
DataReader: No Local storage is required.

Where to use:
Dataset: If you are going more number of operations(updates, inserts and deletes) on database and updates done in batch wise, then dataset will be best option. Use Dataset, if you are going to implement  sites, which are no need of  changes on every client clicks, such as "Carting in shoping mall sites", "display information in websites from database".
DataReader: If you are going to fewer operations and directly implementation of queires on database, the datareader is best option. Use DataReader, if you are going to implement "Booking a berth in Railways", "display current price in Stock Market".

Performance: Choose Dataset or DataReader according to situation, purpose and  uses of database display.