I received the sony e reader as a gift and later purchased an amazon kindle reader for a family member, so I have experience of both products.
The Sony is the smaller of the two items and is easy to hold with one hand, while the Kindle is slightly larger and more difficult to grasp due to the position of the forward and back buttons on the sides.
The Sony is great for reading PDF files as it automatically adjusts the page sizes to fit the display screen. The Kindle struggles with this type of file as you need to page sideways, up and down to view the while page.
I wish I had known before I purchased the the Sony that the screen is not backlit so it is difficult to read in low light conditions. The Kindle is much clearer. Additionally the Kindle is easier to load as e-books can be wirelessly e-mailed to the device. On balance there are benefits to both products. I prefer the Sony for reading PDF files and the Kindle for eace of loading and better visibility.