The two seem to like each other, despite being adversarial. It is likely that the two enjoy having an intellectual equal. On Parson's side, Charlie is independent and one of the only characters who always seems to understand what Parson is saying, whether real world references or leetspeak is used. On Charlie's side, although Parson holds duty to Gobwin Knob, he is not bogged down by any of the prejudices Erfworlders generally have and has an out of the box method of thinking that Charlie can appreciate.
That said, however, considering the potential damage that Parson could do to him, having an intellectual equal is a "pleasure" which Charlie would forgo if he could. Charlie has informed Jillian that he's very concerned that his secrets have been compromised. The most damaging of the secrets about Charlie which Parson has learned so far would probably include:
1: One of Charlie's Rules instructs his Archons to make trouble for their own clients, in order to create new employment opportunities.
2: Charlie has no Warlords or Casters.
3: Charlie never leaves the central tower of his city, which means potential assassins don't need to search the rest of the city to find him..
By the Siege of Spacerock, it is revealed that Charlie is terrified of Parson and is absolutely determined to kill him. He refuses to work against Parson directly, instead striking against Gobwin Knob's interests via proxies, such as Faq, Haggar, and Jetstone, likely to avoid the cataclysmic damage Parson could unleash if things escalate too much. He eventually exposes his hand to Parson at the Siege of Spacerock, taunting him and making things personal.