Netflix versus Blockbuster is a fight that is going on since Blockbuster entered the online DVD rental business. Blockbuster still struggles to win against the pioneer.

Thomas Hawk has a detailed look at both companies and their chance in the DVD rental market. At the end of the report is a response to this report from Wedbush Morgan Analyst Michael Pachter.
With both views you get somehow a full picture.
For you as the customer this does not really matter, besides that at the moment the fight between Netflix and Blockbuster is not reducing the cost further of renting DVDs - We want free movies!

The current offers of the DVD Rental services: