Well the most obvious difference is the colour. White for Naomi & Blue for the Naomi2.
On a more technical note, well lets take a look at the specs...

So basically the major difference between the two systems is the graphics side of the system.
The Naomi2 also boasts a dual-cpu configuration.
On the graphics side, there is a doubling in graphics engines, and the inclusion of a dedicated geometry engine.
So with this increased graphics capability, it's no suprise to hear that Naomi2 games will not run on the Naomi.
However, Naomi games will run on the Naomi2, with no difference in look or performance compared to when played on a Naomi - even if Terry the expert from the pub say's it does - as the code in Naomi games has not been written to take advantage of the extra graphics hardware of the Naomi2.