Just wanna jump in here, when something is "native" that means it runs on a piece of hardware with no software interface. For example, a simple calculator has the native ability to add, subtract, multiply, divide. Now, imagine one of those fancy-shmancy graphing calculators. You can code programs on them in Z80-Basic or whatever it happens to be on the specific calculator, but those programs are "software", not "native."
PSX emulation is something that the PSP is capable of "out-of-the-box", but that doesn't mean it has native support for PSX games. If it had native PSX support, then you could put a PSX disc into it, or in a better scenario, a PSX .iso on your memory stick and it would just run it, no POPSLoader necessary.
From Wikipedia:
The term native mode is used in computing in two related senses.
* to describe something running on a computer natively or in native mode meaning that it is running without any external support as contrasted to running in emulation.
* Native operating system, native instruction set, etc., in application to a computer processor means that the corresponding item was implemented specifically for the given model of the computer or microprocessor, as opposed to emulation or compatibility mode.
Neither of those definitions applies to running PSX games on your PSP. Knowledge is power!
EDIT:
Also, every PSX game I tried personally on my PSP looked on the low end of acceptable. Take that with a grain of salt (or perhaps not, depending) because I've been playing PSX games in 1680x1050 with all kinds of AA and AF with ePSXe, and the PSP doesn't have the screen resolution or processing power to look even close to that good. So, if you've been playing on your PC with a decent or high-end system, you might think your PSX games look a little rough on the PSP. If not, then the best answer is that they look a heck of a lot better than on the PSX or PS2.
EDIT 2:
Also, believe it or not, some PSX games had partial or full widescreen support. The emulators get funky sometimes when it comes to that, but for example if i play Chrono Cross on PS2 on a widescreen TV and i'm using the component cables, it's in widescreen (except for the menu's, which it letterboxes, if that's the right term to use for the bars on the side.)