Travel can be either an intensely personal, soul searching journey or an opportunity to connect to others while seeing amazing sites that bound one another in a shared experience. The choice of whether to travel in a group or on your own depends on your personality type and the experience you want to have. Having traveled both ways personally, I will explain elements of each.
You will pay more attention on your own
When you go around the Louvre and you are on your own you will pay closer attention to the art works. There will be no talking, and by default no personal dramas unfolding, that could possible knock your attention away from the spectacle in front of you. This allows you as the observer to really personalize the moment without any kind of outside disturbance.
When you are on your own there is no one there, with a different agenda than you, that could possibly divert you from the way you want to do something. Other people are great when you are wandering through a city, but differences in bathroom needs, being hungry, and how fast they get tired can lead to two people not feeling fulfilled in the experience. When you are on your own traveling and see different sites, it is you that leads the way and it is you that decide when it is time to move on.
By yourself there is no one to share the experience with
As great as the first two points are, it also is nice to have someone there with you to soak in the experience with too. When you travel alone you see things and they live in you, but they have no chance to be exported to another person to share it with. Now the chance will arise when someone else has been to where you have been, but it still won’t be the same as walking through the coliseum in Rome and having the chance to discuss the experience as it is happening. This last point leads me to say that, an experienced traveler should have both experiences alone and with friends. Each experience is valid and worthwhile.