If you like both, you should do both. However, a lot of people who do the alternate aren???t really doing anything if they???re holding the weight at a lockout. More often then not, when I see people doing alternate db chest or db shoulder presses, they have the non-pressing arm locked out. At that point it???s your triceps maintaining a joint lock and not your muscles (chest or shoulders [w/tri???s], depending on what you???re doing) holding the weight in a static contraction against the weight. If you hold the weight with a slight bend at the elbow, then you???re getting a good static contraction in there, mixed with the isotonic movements.
Pro???s of alt presses, you mix up the muscle stimulation, you get your concentric, eccentric and static contractions. Con???s, you tend not to achieve as many reps, because a true static contraction (not locked out) will wear down the muscles intra-set stamina.
It boils down to new stimuli. Either you???re creating greater stress by going deeper with the reps, heavier with weights, or you???re creating greater stress by adding the static contraction with alts, everything has it???s place in it???s own season. Personally, I prefer regular lifting. I don???t care for getting too, too exotic. One isn???t superior to the other in an absolute manner, because no matter what you???re doing, your body will adjust, and the new thing you try will become the more effective thing, until your body adjusts, then you go back to the old thing and that becomes more effective again.