To understand why PSP "won" Leipzig, I think it'll help to see why the other consoles didn't fare as well.
Why PlayStation 3 didn't win
Was PlayStation 3 even there? Sony didn't enter this round, and they're placing all bets on the Tokyo Game Show. I guess the PS3 has a prettier version of Virtua Tennis, but I don't think that's worth talking about. They DID have Metal Gear Solid 4, but it certainly wasn't anything new over their already-impressive E3 showing.
Why Xbox 360 didn't win
Of the three next-gen consoles, Xbox 360 pulled by far the most impressive showing. Scoring next-gen exclusivity for soccer games (at least this year) is a huge win for Microsoft, considering how there are many people (myself included) that are in a post-World Cup depression. But what else was there? A laughably bad presentation of Rare's next game... and not much else. I'm excited for Settlers of Cataan (seriously) and Lost Planet, but there was nothing really new that grabbed my attention.
Why Nintendo Wii didn't win
After such a huge presence at E3, Leipzig was a disappointment. Why? We still don't have a price or a release date. These are the basics, Nintendo! Stop teasing us like that! Battalion Wars 2 and a new Super Mario Strikers game was announced, but these aren't really high-profile games. Red Steel has gotten a lot worse graphically from its computer-rendered lies.
Why Nintendo DS didn't win
The DS had a lot of games, but none of them are really heavy-hitters. Lunar Knights returned and was (unsurprisingly) good. As this games reel shows, there's a lot of excellent games coming out for the system, including Pokemon: Mysterious Dungeon and Yoshi's Island 2, but these were all shown (and playable) at E3.
So, that leaves us to our inevitable conclusion:
Why Sony PSP won Leipzig
Sony didn't come to support its hardware or its games, but Konami completely represented for our handheld. You had smaller name games, like Death Jr. 2 and Coded Arms, but you also had two of the biggest games at the show: Silent Hill Origins and Metal Gear Solid... and both are PSP exclusive titles. Silent Hill features some stellar graphics, and that game is very early in development. Metal Gear Solid features a more extensive multiplayer component than its console prequel, and features the "best script ever" for a Metal Gear game ever. It was playable and while it's a little shaky, it offered something new for the Convention. Yes, other platforms may have more big-profile games coming for it, but no real new news came from Leipzig. Konami showed there's stil a lot of life left in this system.
I think you should take the "PSP Challenge" (a la Pepsi Challenge) and show your friends footage from these recently revealed games. I know I surprised a lot of people, who have forgotten that the PSP is capable of really beautiful graphics. Remind people that these are new and exclusive offerings of the handheld, and you'll see a lot of people's opinions start to change about the system. It's really easy to bash the PSP, but now's your chance to really educate these people about why it's a great time to get excited for the PSP again. With such an excellent showing at Games Convention (even without the support of Sony!), Tokyo Game Show is going to blow us away... and I can't wait.