vinnyb,
The simplest and safest solution is for both of you to hold down the shift key while CivIV is starting. This fixes the problem without you needing to dig through folders and potentially delete the incorrect stuff.
Not-so-important stuff about this that you don't need to know but you might find interesting:
The problem is caused by the RNG (Random Number Generator), mostly in the random events, but also elsewhere where the RNG is used. What happens is that when someone installs a fresh game and upgrades from 3.00 (base BTS install) to 3.13, the game writes different information into the folders than when someone else upgrades from 3.12 to 3.13. While playing the game, each version locally runs the RNG to see what's going to happen. Normally they both use the same random number seed, but if they're different you'll get different results such as different random events, or 1 person gets a barbarian spawn while the other just sees a bandits attacking their farmlands, or even different combat results.