We've mentioned this sort of thing in the Showcase Forum before.
The best thing is to have clearly defined rules of what is acceptable and what is not acceptable behavior and enforce them (as a team).
That being said, approach the person privately and state that is the board's policy not to allow any spam-like threads and ask that they refrain from doing so in the future. Better to approach them privately than making a public scene by banning someone right off the bat.
You don't want to put any negative image on your site and what you have worked toward, and certainly don't want any conflicts between competing communities aired in public. The other person may see this as a way to drive a wedge in your community.
If the person refuses to stop, then you need to edit/close their posts and if that still doesn't stop them then remove their posting privs for a while. Still a problem, then a ban is probably the last resort.
If you are consistant with you policies, your members will be understanding.