The Sun
Nicole's Sun is in Virgo, and Paris' is in Aquarius. Paris has a streak of unconventionality, originality, and need for novelty, while Nicole is more cautious and conservative. When together, Nicole's criticalness and fear of making mistakes can put a damper on Paris' fun, exploration and free spirit. Put another way, Nicole prefers order, while Paris thrives on a bit of chaos, often causing it for her own amusement. Nicole is a pragmatist, while Paris is an idealist.
Mercury
Both of their communication planets -- Mercury -- are in compatible air signs, which tend to be mental. These gals solve problems and think about issues with a similar perspective (however naïve and/or warped) and are able to communicate clearly with each other.
Venus and Mars
Paris' receptive Venus opposes Nicole's active Mars. They have a warm, affectionate relationship but there are strong elements of rivalry and competition between them. Nicole tends to be the more assertive one in the friendship, and may try to dominate more than Paris would like. Paris sometimes gives in to Nicole too easily. A good, honest fight or strong expression of emotions is actually good for them every once in awhile, otherwise tension and actual dislike will develop between them. Since these ladies seem to have mended their highly-publicized rift, it would seem the big blowout was the best thing that could have happened to them and also to the producers of 'The Simple Life.'