Phat.
The Slim has lower compatibility with homebrew, and no IR which means no use of a PDA keyboard, as well as fewer accessories. The only thing it has that the Phat does not is more RAM to work with and only one or two programs (that I know of) actually utilize it. The Phat can have TV Out as well, if you purchase and install the PSP2TV addon. It is not any more difficult than replacing the analog stick or screen (both of which I managed to replace with no real hassle). Of course, the PSP's screen is so big that a TV Out feature is notr eally necessary unless you happen to own an extra large high definition TV, which is still quite uncommon.
I recently broke my Phat PSP and purchased a Slim to replace it, and I have been regretting it ever since. I may shell out the money for a Phat again in the near future.
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