which is better barbell bench press or dumb-bell press, and why?

Their both good. The only difference – and what might make your opinion, is the body parts that each works out. barbell bench pressing works out on the chest mostly, with lesser degrees on the biceps, triceps, and back. Barbell presses – I’m assuming you mean different routines than from pressing as if it were one bar, works more on the arm muscles – biceps and triceps, and less on the chest.

You probably want more effect on your arms. Therefore I guess you will like dumb-bell press better.