I have a Galaxy Player 4.2 and a 1st gen Fire. Ok, and a kindle keyboard too, but that has mostly been passed on to my spouse.
Having access to Google Play via the GP is a nice feature and has allowed me to sideload a few good apps on the Fire. The GP makes an awesome PDA and is okay for reading in a pinch. Gmail works great and with the SD slot, I can easily carry my music collection around. So I use it most for PDA functions, very light web browsing, podcasts, and music. The GPS functionality is pretty good for a device lacking 3g. Night reading sucks on the GP because of the lighted Back and Menu keys. They cannot be dimmed and are bright and jarring in the dark. I prefer email on the GP over the Fire because I can use Swiftkey whereas you're locked into the mediocre Kindle soft keyboard. The portability is incredible. Makes the Fire seem huge in comparison.
GP camera is not good. Would not advise buying it based on the camera.
The Fire works well for reading, pdf annotation, web browsing, and occasional gaming. Evernote is a godsend for organization and task management on both devices. The ultraportable PDA features and the SD card are the biggest benefits of the GP. Google Play access is nice but not a huge thing for me.