If you really think about it, the correct answer to your questions is . . . It depends! It depends on which Playoff format you're using. If the Big 12 continues under the current four team playoff format, doing away with Divisions and playing a round-robin schedule with your top two ranked teams playing in the Conference Championship is the better option than going with Divisions. But, at some point in the future, if they go to the anticipated 12 team expanded playoff format, you'd be better off going with Divisional play, and here's why . . .
Under the current four team playoff format, the principal focus of all the Conferences (except for perhaps the SEC) is getting your conference champion into the playoffs, but if you go to the 12 team expanded playoff format, your focus completely changes. It will now become focusing on getting your second team in to the playoffs, as your best team (Conference Champion?) will be in the playoffs, no matter what, with the new AQ conference bids.
Proponents of doing away with Divisions and going with the "round-robin, two "best" teams in the championship game" idea always cite the benefit of giving your highest ranked team a boost to get them over the hump into the top four playoff slots by providing them an extra "quality win" opportunity at the end of the season by having a more compelling Championship Game. But with the expanded playoff format and the inclusion of the AQ bids, you don't really need that "quality win" anymore. so that takes away the main benefit of having your top two teams always playing in the Championship game.
What you need to do instead is to protect your Number 2 ranked team (the one you're actually trying to get into the playoff now) from suffering a late season (and unnecessary) loss that could potentially drop them out of the top 12, and therefore out of the playoffs, by forcing them into an extra hard game by playing your conference's best team every year. You would potentially protect them by having the two Division champs play in the Championship game, as opposed to always playing your two best teams.
Let's look at a very plausible scenario that highlights my point. This scenario closely mirrors what happened to the Big 10 this year, with Ohio State playing their fourth best team, Iowa, in the Championship game, instead of playing their second best team Michigan!
Let's say that the Big 12 has gone to East/West Divisions after the four new schools have joined, UT and OU have left, and the new expanded playoff format has started. The last CFP ranking has just come out the week before the Big 12 Championship game is to take place and the highest ranked Big 12 team is Cincinnati, from the Eastern Division, at #5, your second best Team, Baylor, also from the Eastern Division, is at #11, and your highest ranked team from the Western Division (Oklahoma State lets say) is at #15. If your 5th ranked team (Cincinnati) is playing your 15th ranked team (Oklahoma State) in the Championship game , instead of playing your #11 ranked team (Baylor), you're saving Baylor's #11 ranking by not having them play a 13th difficult game, which they would more often than not, lose and potentially get thrown out of the playoffs by getting them dropped back to #14 or #15!
Having a 15th ranked Oklahoma State team suffering another loss won't really hurt your conference because they were already out of the playoffs. Another loss would only make them slightly more out, whereas another, more than likely Baylor loss, would cost the conference a couple of million dollars! On the other hand, using a divisional setup in this instance could provide an additional benefit in the unlikely event of an upset, where you could potentially get, all three teams in (Cincinnati is now at #8 after the loss, Baylor still at #10 or #11, and Oklahoma State is now at #12 after the win)! But that "best case" scenario only happens with a divisional format!
But if you want to alter this scenario slightly and place your second ranked/best team (Baylor) just slightly outside the playoff range at 13th, where they could use that late season "bounce" to get into the top 12, the only way not utilizing a divisional format (round robin) would pay off is that you'd have to always hope for a more improbable "upset" to occur! Additionally, if the Big-10, ACC, and the PAC-12 all elect to do away with divisions, the #2 teams from those three conferences will probably be in the 9, 10, 11 range, and if any of those #1 vs #2 Championship games don't result in an upset, that conference has just shot themselves in the foot, and the Big-12 would benefit by not doing anything!
My basic point is this, that if you're playing the percentages to give your conference a slight edge, your chances/percentages of getting a second Big-12 team in a 12 team playoff format are better (even if only incrementally) if you're using a Divisional setup , as opposed to a round-robin setup!