One on one it would be no contest.
JaJuan will surprise people with his speed, quickness and strength. He can shoot over BBD Dunk over BBD and blow by BBD. BBD may be able to back him down; but JaJuan will just swat away anything he puts up.
I would think that the opposite would happen.
JaJuan was known as a guy with really poor lower body strength who frequently got out-muscled in the post at the collegiate level. I think BBD would push him around easily and create high percentage shots around the baskets.
On the other end, Glen Davis' quick feet (laterally) and physical post defense would make it difficult for Johnson to either beat him off the dribble or post him up. BBD would be able to effectively push Johnson off his favourite spots and into lower percentage shots out of the post (even though Johnson can clearly shoot over the top of BBD).
And if I am remembering correctly, despite JaJuan posting big scoring numbers in college and scoring a lot out of the post, he only did so on a barely above average scoring efficiency. Having someone like BBD who can push him off his favourite spots would make life difficult for him.
But anyway ... one-on-one skills don't matter much with either guy because neither will be asked to do so on this Celtics team in the immediate future.
I think JJJ's length, athleticism and shooting range will make him a much more effective complementary offensive threat than BBD has been.