If you first owned a Sony and subsequently purchased books through the Sony store, they could not be read on any other device. If ou first owned a Kindle and subsequently purchased books through Amazon, it is possible to read on other devices but the DRM must be removed from the ebook. The ebook may or may not need to be shifted to a different format to be read on another device. The books would be of the same quality after reformatting.
In my experience, most libraries offer more pdf than mobi. Some libraries are beginning to offer epub. For the Sony, assuming you have a card for your local library, one would check-out the book from the library, the ebook would download and open in ADE (Adobe Digital Editions), then it's a simple drag and drop to your Sony Reader. Borrowing mobipocket books from the library requires an extra step which I'm not familiar and will let others speak to that.
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