Difficult to make a list as I have only a Slim, but...

The differences between the two are the Slim's naturally lower size, weight, brighter screen, twice as much RAM compared to the phat, and other smaller cosmetic changes and whatnot.

Though, in terms of homebrew, the phat still has the best compatibility due to it being out longer and more people (generally) having it over the Slim. But I've been fine with all emulators that I've tried apart from the SNES one, so that's not saying a whole lot. I'm pretty sure the Slim also has the TV out support though I may be wrong here. It only goes for...hmm..whichever isn't Red/Yellow/White outputs for TVs. I'm not sure how the GBA emu works, but seeing how I have no need for it, I'm useless here too. =P

To mod either, you should really only need a Pandora battery (either premade or modded), and a memory stick you can turn into a Magic Memory Stick to install custom firmware (CFW). You can use the stick you're going to put games on, as long as that stick is at least 128MB in size as the NAND which you need to back up (and should anyway) takes 66MB, and it'll corrupt your stick if you use a 64 megger. And, you won't need to really need the functionality of the MMS unless something goes horribly and I mean HORRIBLY wrong. Same goes for the Pandora battery too.

We have a couple of still-relevant topics here to get you started on modding. As for pricing, if you do it yourself, the price will be the same for both, but remember that if you get a premodded Slim battery, it will only work in the Slim, whereas the phat battery will work in both models (though on the slim you can't use the battery cover).

 

http://gbatemp.net/index.php?showtopic=68111 Will answer your questions

 

@above: Daedalus R13 runs fine if you use the 1.00 firmware version. (IDK about those other versions though)
Making a MMS is as simple as downloading 2 files and clicking a button.
NAND memory is NOT used for emulation purposes. Normal RAM is.

 

I have two slims and a fat. Fat's are better made, in my opinion, but the slim's the better machine. Latest slims cannot be modded with current pandoras according to reports. I would buy slim, in my opinion.

 

then if i get a slim how am i suppose to modify it ? to be able to use emulators etc . ?

 

grr . so i guess it might be best to buy a PSP Phat off of one of my friends . reliable and you can trust them .

how about the limited edition god of war PSP ? can you use the pandora batteries on that ?

 

Theres not a lot of psps left, took me like 5 stores to find one..