Zeller
Lakers got too many similar type players at PF/C with Jordan Hill, Ed Davis and Julius Randle. Carlos Boozer is the only skilled big man on the roster. As such, Boozer should receive major minutes because he is the only player who provides offensive integrity to team. Hill will be the starting center as he is the only one of the other three (unskilled bigs) with enough size to play long minutes at that position.
That leaves the other two bench players - Ed Davis and Julius Randle - those two will have difficulty finding effective combinations / lineups because of their combined lack of skill-level offensively (and also J.Hill's). So minutes and consistency of playing time, role, placement in position where they can succeed = all problematic. I wouldn't be surprised to see Ryan Kelly beat out those two other bench bigs for playing time because LAL will need Kelly's jump-shooting and passing to keep defenses honest.
LAL is just another bad situation for Ed Davis to be in. He needs a skilled center alongside him to get long minutes (more than 15-20mpg) due to his limited offensive game.
So Tyler Zeller should win this comfortably. His extra size allows him to play center unlike Ed Davis and that will allow him to get on the floor for more minutes and be of more use to Boston than I expect Ed Davis to be in LAL. Good chance at starting job. Should be a regular and productive (versus problematic = Ed Davis) bench player even Tyler Zeller fails to win starting job.