I learned/am learning English with heavy self-study, and recently I have taken 2 classes. The classes helped a lot.
I definately could not have learned on my own, because there are few English speakers in my area.
So I have to find a place I can practice a lot, and I actually did.
You can learn reading and listening by yourself, but when it comes to speaking, it is nearly impossible.
Real speakers ask you unexpected questions, and that makes you find out your week points, what you have to go over again.
I learned Spanish in a class, and I'd say it's definately better to do that.
Learning verb reflections from books/DVDs alone was nearly impossible for me.
Besides, I had no Spanish speaking friend from whom I could learn in person.
So I'd say it depends on location, what's available to you, whether you can motivate yourself.
Self-study should be best prioritized on a daily basis while classes complete what you are missing.