If the deals are close, ship him to the AFC. If there is a significant difference, ship him to the best offer especially if you think the shelf life of Rodgers is 1-2 seasons anyways. One of those seasons will be this year where the Packers are probably not a realistic SB contender so, if he helps some NFC team win this year (that isn't in our division), who cares.
Plus, if the 49ers, the Packers could spin it to a PR 'win'. "We appreciate everything he did and gave him the chance to play with the team from when he was a boy"