There's pros and cons with both.
On your own you don't have to compromise, go where you want when you want, change plans on a whim, stop when you want... You also tend to meet more people, you get into conversations with strangers that you wouldn't have if you'd been in a group. You do have to be more self reliant, there will be times when you feel it's be nice to have someone to share with. And there's no way of splitting any luggage!
In company it can be far more social with many things the opposite of above. If you're not careful you can end up doing exactly as you would at home, just in a different place.
There is a third way!
I've recently had a 8 day tour of West Scotland with a friend. We have different interests and wanted different things from the tour, all agreed before hand. We stayed at the same places, spent a lot of time riding together but without the obligation to stay together. If he wanted to go and see something I didn't off he went, if I wanted to go earlier in the morning I did. If I wanted to go for a blast up the A road and he wanted to do the scenic route, that's what we did. It worked pretty well but has to be understood in the planning stage.