One of the best and obvious advantages to homeschooling is the speed at which the children learn and the amount they learn. I have realised that, left to themselves, children learn a lot more than through a structured approach. In fact, is that not the case with all of us? That is why adults seem to make better learners. Because once they get out of structured learning, they find themselves more motivated to learn since they are doing it for themselves rather than being told to do so.
Another advantage that I have seen is that since the children are not under any kind of pressure, they seem to outsmart themselves all the time. In fact, they enjoy the competition from within. In a formal school environment, it is always an issue of superlatives. Who is the best! Here it is more comparative. It is 'have I done better than last time?' And, I think, that is so important.
If there is an offside to homeschooling then the only thing I noticed when we began learning at home was the lack of discipline. But, again, I was viewing discipline from my definition of it which is largely influenced by the school system and the educators therein. But it did not perturb me very much since I knew they were going through their period of adjustment to a new way of learning.
Do the kids enjoy this kind of learning? I think they do a lot. Humans hate structure even if we have accepted it as part of our lives. But we are always striving to fight it. So, the children too are enjoying the flexibility of learning what they want, when they want and in the manner that most appeals to them. But, being animals of habit, I have encouraged a schedule since, after all, one day they will need to fit into this world.