The PSP can run emulators, but it itself isn't an emulator. Emulators are software (and sometimes hardware) designed to mimic another system to put it simply.
Android is fine and dandy, but they tend to be lacking in the controls department. Yeah, you can carry around a Bluetooth controller or an attachment, but it just makes it far too bulky for my taste. PSP is great for someone just wanting to run emulators up to the GBA and PS1. In my area, you can find an old Phat for $30 to $40. Of course, if the OP wants to emulate anything more powerful, he's better off with any newer smartphone or tablet, it's just they'll be far more expensive. Heck, even the Pandora emulates the N64 decently, with enough tweaking.