If you had the same kind of device (or more exactly the same ebook DRM), it would be perfectly legal to share ebooks up to the limits set by the DRM (which is 6 devices for the Sony and Kindle). Since you have different kinds of devices, it is on its face illegal under the DMCA in the US to strip the DRM to share ebooks. I would still describe this a personal use, but I am less sure this is legal in the US (even though it is exactly the same act as the DRM allows for like devices) than I am that one individual can legally move a ebook from one device to another.
In any case, as a practical matter the Sony LRX ebooks can't be used on any other device types. The Kindle AZW files can be converted to DRM-free MOBI files if you know the Kindle's PID (
kindlepid/kindlefix 0.2) using mobidedrm. Another option is to buy Adobe ePub, e.g. from Books on Board, which is readable "as is" on your PRS-700 and can be made DRM-free (
Adobe ADEPT DRM for EPUB circumvented). A DRM-free MOBI can be converted to LRF or ePub using Calibre, and similarly a DRM-free ePub can be converted to MOBI (for the Kindle) using Calibre.
EDIT: some Kindle AZW files come DRM-free. The easiest way to tell is to try to convert them to LRF using Calibre. Calibre is very easy to use. Stripping DRM requires some familiarity with python scripts.