I got the OG model but the screen is the only benefit it has.
The slim is lighter, has larger grips to accomodate your hand, has better battery life, comes with 1GB of internal memory (OG has none, so without a memory card you can't even save any game) and doesn't use a proprietary charger plug anymore, it also has the best overall design IMO.
The OG has the better screen and I love it looking like a psp and being all glass up front (Slim is only for the screen).
So I got the OG anyway because the OLED is so much better than the LCD screen and I love it feeling like a perfect PSP (great screen + two analogs, all the PSP needed). XD
I got an original one this year and I'm starting to regret it, since I had the option to get an Slim. The Rear Touchpad is waaaaay too big, it's not confortable for me to hold it for long play sessions because of this. The screen is amazing though.
I also have an original, went out of my way to find one about three years ago, with the grand total of one game, but yeah it is very heavy and thus uncomfortable and the rear touch pad gets in the way. If those things are addressed then that is a plus.