Working with DB's will insure an equal balance for both side of the body, muscle and strength wise. DB's will give a fuller stretch or ROM in some movements. One example is the flat/incline bench. DB's allow a more natural twisting of the wrist and the following of the muscle/joint function better. A straight BB may set the wrist in too firm a fixed position. One reason that big benchers, using a BB, may have a better potential of joint/shoulder injury. More variety, angle recruitment and extension exercises can be done with a pair of DB's. A EZ bar can allow more relief, over a straight bar, in some exercises. A example would be biceps/triceps & up-right rows. A EZ bar would be closer to a DB, that a straight bar would, by the different set gripping angles.
A straight bar would have the advantage of using the heavier Big Boy exercises to their fullest advantage: Squats, DL's, rows, benches, etc. This would include rack training, partials and lockouts. A straight bar can direct better focus on a lift for a lot of guy's. Using max weights with a BB will tend to give the max results back to the trainee, producing the better gains overall. If you are training with serious intent, than a combined workout of both a BB and Db's should be the best option, for reaching muscle size potential.
Cable work also has a role in achieving muscle size. The best of non BB/DB movements are done on a chinning and parallel bar. I believe (for whatever it's worth) that anyone could achieve outstanding upper body development by just using a chinning and dipping bar,alone. With added weight, of course. Any trainee should mix up the equipment as much as they do different training programs for ultimate results. Good Luck.