PS1 emulation on the PS3 is a purely software affair, so any PS3 can do this.
PS2 emulation does require extra hardware, it cannot be purely emulated by software. Here's a rundown of how it was achieved:
In the original US and JAP PS3 consoles at launch Sony included a single chip combining the PS2's Emotion Engine (CPU) and Graphics Synthesizer (GPU). This allowed the launch consoles to run just about any PS2 software you through at it.
For later US models and the UK 60GB launch model, Sony removed the Emotion Engine and just have the PS2's Graphics Synthesizer in silicon. By this stage, they were able to emulate the EE in software. This did add some compatibility issues with the backwards compatibility, but would still run the majority of software.
Then as the final cost cutting measure the GS was removed from the PS3's design, thus ending all PS2 backwards compatibility. As K1LLSW1CH has said PS2 games on the store are modified to run on the PS3 - they will be recompiled/ported for the PS3 architecture)