There will be a tie for the regular season conference title (you will both be conference champs).
In terms of conf tourney seeding, the answer is on the FAQ:
A: Overall Conference record, at the conclusion of the regular season, is used to seed teams number 1 through 6 by division. The teams will then be split up so the #1 seed from division A will be in the same bracket with the #2 seed from division B and so on. The following procedures are set up to establish seeding for the championship and to break ties. Follow the appropriate steps in order.
Two-way Tie: (2 teams in the same division conclude the regular season with the same conference record)
1. Regular season head-to-head results (one game or two). If the tied teams split their two games, then proceed to Step #2 below.
2. Overall record. If the tied teams had identical overall winning percentages, then proceed to Step #3 below.
3. RPI ranking