In the past, Netflix has seemed somewhat resistant to competition, at least in part due to their patents for using an automated queue of movies to be delivered and selling subscriptions to rent a specific number of items at a time. They've even managed to not only compete with Wal-Mart, but even get the retail giant in their corner after the fight.
If they've shown a weakness in the past it's been in the time customers have to wait for their DVDs. In 2005 they settled a class action lawsuit regarding their claims of 1 day delivery times and unlimited DVD rentals. One of the biggest complaints from ex-customers is that Netflix uses a technique known as Throttling to penalize subscribers who don't make them as much money by making them wait longer for their DVDs. After the lawsuit was filed they denied those claims, but eventually changed their terms of use to specifically allow it.
Blockbuster's approach, on the other hand, takes advantage of something Netflix doesn't have - over 5,000 brick and mortar stores throughout the United States. Their rental plans include some where movies can be returned to their stores and even get a Limited number of free rentals there.
Netflix has responded to competition from Blockbuster by adding a Streaming media service that's automatically available with their subscriptions. Unfortunately this service requires an internet connection with a minimum sustained download speed of 1Mbps for low quality video or 3Mbps for near DVD quality. Still, for people who don't want to visit a retail store, or don't have that option based on where they live, it's still a big improvement over a minimum 2 day wait to receive their movies through the mail.
For consumers this has turned out to be a win-win situation. With both companies focusing on competing with the other, their customers have benefited from additional services that come at a lower price. Much like the well publicized battles between Intel and AMD for CPU dominance or nVidia and ATI for the graphics card market, no matter which company is ahead on any given day, arguably it's the public who are the real winners.