OverDrive doesn't work on Kindle. Also, many libraries have only a very small number of OverDrive books: my local library has 30 ebooks on OverDrive.
I will echo that most OverDrive collections are nowhere near large enough for most people to care just yet. But that has been rapidly changing with so many compatible eReaders on the market. Libraries are just now bulking up on digital licenses to meet the surging demand. I would not be surprised if there are already libraries with more digital copies of a popular novel than paper copies.
[1] http://overdrive.com/news/OverDrive-and-Amazon-launch-Kindle...
[2] http://www.amazon.com/gp/help/customer/display.html/?nodeId=...