With the split, Netflix gets to focus entirely on streaming - make it better for the customer. Which means, more (and better) content, faster and better streaming service, Netflix on more devices, providing Netflix outside US and Canada etc.
And Qwikster gets to focus entirely on DVD service - which means expanding the DVD catalog, getting video game rentals for Wii, PS3 and Xbox 360.
As a customer, you get a much better Netflix and/or Qwikster experience. As a Netflix employee, I get to focus entirely on making streaming better, faster, available on more devices, and in more regions than we have today, without having to worry about compatibility with the DVD service.