Depends on your aims - I was trying to get to L4 missions, so I always took rewards with char1 and kept the rep/reward for him. When he hit L4 missions, I started sharing the rep so that my alts would eventually get up to L4, allowing me to be more selective on mission acceptance (ie. don't like the L4 mission offered to char1, reject it, don't like the alternative either then just move to char2 and see what he gets offered etc).