I think there are actually a number of ways you could quantify this in game.
Free agent signings is one, a better manager can sway a FA. Some in the media think the Cubs will have an easier time courting FA's now that Maddon is on board since he is very respected around the MLB. Typically a player will take the most money, but since The Show uses an interest system for the offseason logic I think this might make sense for the game. I've had players decline contracts when I'm offering way more than the next team for instance.
Defensive shifts is another one. Some managers believe in them, some dont. Most acknowledge shifting is necessary, but not all go as crazy as others. I hope defensive shifting becomes a bigger part of the game in MLB 15. It is a huge part of the MLB strategy now and I'd like to see AI teams use it much more often.
Manager challenges are another one, especially if this makes it in for MLB 15. Some managers challenge more often and some are more successful in picking their spots to challenge. (Renteria:25/57, Hurdle:20/35, Farrell:19/34, Girardi:23/28, Showalter:14/28) Could be luck, but could also mean a lot in terms of a manager and the team's ability to pick when to challenge.
Bullpen use is another big one. Does a manager believe in using a RP for >1.0 IP? Does a manager believe platoon trumps all other strategy? It would be cool to see this in game, even if this was randomly assigned to managers, just for diversity in strategy. How about defensive subs? Does a manager believe in always subbing in a defensive LF, RF or 3B when having a lead in the 9th inning?
Lineup logic is another one. Many thought Renteria was strange in that he kept Rizzo 3rd and moved Castro to 4th, instead of the other way around. Some question Matheny in using Carpenter at leadoff when he could be more valuable 2nd or 3rd in the order since he is more than just a walk machine. If every team has the same lineup logic that sort of makes stuff boring. In game Carpenter routinely bats 3rd when I face the Cardinals and Castro leads off. I think that shows that there are varying beliefs in how a lineup should be constructed between people.
I get that many think managers don't make a ton of difference, but FO's and players sure do think they matter. I'd love to see it make more of a difference in the AI of team strategy, offseason logic, trade logic, player happiness etc. If you are going to make it a point to have players sign coaches and managers in game, make them relevant to the gameplay. Otherwise they are just for show, other than the slight + and - they bring. It's not a big issue at all with the game, just another thing that would add to a great game and make it feel more alive.