Even though listening to music in the comfort of one's private space has its advantages, going to concerts is great from at least two perspectives: enjoying good music and getting more involved into what is going on, through sympathy, as one cannot remain indifferent to the visual spectacle that makes one react mostly the same as the interprets.
Tension, relaxation, enjoyment, fun might be experienced and emphasized when you also have the view of the finger-tips' strikes on the piano keyboards, the well-shaped muscles of the cello or the violin players' arms, the jumps and the steps on the floor of the conductor.
By comparison, it is like watching a movie. For instance, while one watches a dramatical scene and hears certain sounds that goes along with it, such as drowning or being on the verge of drowning, as a spectator, one feels like not being able to breath as in the images, while the moments are stressed by the music.