Oddly enough, these are the only two devices I've really had experience with. I had a PRS-350 for a couple of weeks, then returned it and got a Kobo. I detailed my reasoning in
this thread.
In summary, I like the Kobo more as a reading device. As an electronic device, the Sony is heftier and feels more solidly built, but the Kobo feels nicer to read with, particularly while lying in bed (which makes up the majority of my reading time). One thing that I love about it (even better than paper books) is how the big bezel at the bottom can be buried in a pile of blankets without obscuring the text.
I've found the screen on the Kobo to be better. Perhaps the Sony has better contrast objectively, but the Kobo seems to have a paler background that is easier to read in my view.
I thought I'd like the dictionary on the Sony, but it turned out that most of the words I wanted to look up weren't in there and I had to use an external dictionary anyways. YMMV...