Are new PSP 3000 games backward-compatible with the PSP 2000?

I was talking to someone who wanted to sell his used PSP-2000 model. He told me that whatever games are played on the PSP-3000 can also be played on the PSP-2000. I wasn't so sure about this so wanted to confirm. I did some Googling and noticed that wherever they mention PSP games they don't mention compatibility with PSP-2000 or PSP-3000, so here are my questions:

1. Does anyone know whether ALL PSP-3000 games can also be played on PSP-2000? If not, how can I find out?
2. What are the drawbacks of the PSP-2000 versus the 3000?

From this Gamespot article

The PSP-3000 plays the same games and offers the same media support as the older PSP models

So all the games are backwards compatible.

From Wikipedia

the PSP-3000 ... has an improved LCD screen with an increased color range, five times the contrast ratio, half the pixel response time to reduce ghosting and blurring effects, a new sub-pixel structure, a microphone, a new disc tray design, new button designs and logos, and anti-reflective technology to improve outdoor playability. It can also output all games by component or composite using the video out cable.[77]

So it's better. The biggest improvements seem to be the reduced ghosting (which still exists but is well, reduced) and the anti-reflective technology.

All current PSP games are compatible with all current PSP models (PSP-1000 "original", PSP-2000 "Slim and Lite", PSP-3000 & PSP Go) . There are only slight hardware differences between them related to screen types, battery life and speaker/microphone type and placement. Some non-game apps need specific hardware (built-in microphone for the Skype app, standard accessory port for the GPS and camera modules) that are only on some models.

The only exception to this is the PSP Go, as this doesn't have an optical drive inside it can't use any games on UMD discs, it uses downloads from the PSN store only, but these are all exactly the same downloaded games that can play on the older models too.

Some software (and most UMD videos) are region-locked, but that shouldn't be a problem if you and your friend are in the same country.