Why not make things interesting and limit polymorph forms to core-only for the Core Wizard and non-Core for the Other Wizard? Since the whole point is to (dis)prove Core > Splat, shape-changing into non-Core things is not a constructive argument.
Magic items...guess both should be just DMG (and maybe MIC), just to keep things simple/sane. Banning anything that emulates a spell effect (candle of invocation...), just to make the Wizards use their spells, though wands/staves should be fine as long as you stick to spells you would be allowed to learn under the challenge.