From Starting Strength:
The dumbbell version of the exercise [...] involves a greater amount of instability [...]. This is especially true if the weights used are sufficiently heavy to challenge your ability to finish the set. Most trainees use dumbbell bench presses as a light assistance movement, and never appreciate how hard they are or how useful they can be at heavy weights.
[...] the lifter has to take the dumbbells out of the rack or off the floor, get into position on the flat bench, do the set, and then get off the bench with them after finishing it.
Because dumbbells are not tied together between the hands as a barbell is, dumbbell bench presses require more active, conscious control, are harder to do, and therefore less commonly done.
The problem with dumbbell bench presses is that the equipment provides its own limitations in a progressively increasing program. Most dumbbell racks are not graduated in fine-enough increments due to the expense of having twice as many dumbbells as most gyms have the money or space for. Plate loaded dumbbell handles that would permit such loading are not widely available, or of sufficient quality that they are safe at heavy weights, or capable of being handles without a lot of help from two spotters.
And with heavy weights, getting on and off the bench becomes such a large part of the task of completing the set that the logistics are a giant pain in the ass.
[...] as good an exercise as the dumbbell bench may be, you will be bench pressing with a barbell, as the weight of history and precedent demands.
In my experience, the limiting factor at heavy dumbbell weights is the constant firing of smaller muscle groups needed to stabilize the heavy dumbbells.
Generally, improvements in these small stabilizers don't transfer into sports as much as improvement in the larger muscles. I stick with the barbell, so that I can continue strengthening the largest muscle groups in a linear progression for a long period of time without being impeded by my weaker stabilizing muscles.
The smaller muscles are still getting worked, just not as much, and I'm not letting them be the bottleneck, because that's not where the biggest return on investment is going to come from for me.