Another common comment you hear in the gym and the clinic. For some people the fixed bar path may lead to shoulder issues, but using dumbbells does not always resolve that.
If you do not have good form, upper quadrant mobility and stability either one of these exercises can cause problems; using a barbell or dumbbells.
The problem with dumbbells is that when you work in the heavier, think 1-5 reps, range you spend more energy stabilizing the weights than actually pressing it and if you have difficulty stabilizing the weight you are prone to injuries.
So, sometimes dumbbells might better; other times stick to the barbell, especially if you start lifting heavy weights. The depth of the bench press, may cause more issues that using a barbell versus a dumbbell.
Do you have pain?