Yes and no, say some comparison videos that hit YouTube yesterday. In the startup (above) and DVD loading, you see the Slim marginally trails the Phat. But in starting and loading Batman: Arkham Asylum, it's faster.
DVD Comparison - PS3 Slim vs. Phat
Batman: Arkham Asylum - Game Bootup and Level Load
The Slim's bootup doesn't include the jingle and the Spider-Man font splash screen, but the level load also is faster, so the absence of that probably isn't why the Slim's faster in this test. But who knows.
It makes little sense that the new unit would have a different, slightly underpowered motherboard, so the rumour is that the two configurations might have different hard drives. The maker of the comparison claims both consoles use the same hard drive. It could also be a firmware issue. Who knows.
But look! Look at that! Why the Phat is practically done with the FBI warning before the Slim even shows it! Seven seconds saved! Go Phat! Go!
PS3 Slim Slower than PS3? [Sankaku Complex, thanks Sanjo]