In my opinion, artists on independent labels produce music that has a lot more freedom and authenticity to the artist because they tend to have more flexibility with what they want to be putting out. That being said, there are a huge number of amazing bands and performers out there on major labels that also create a very high standard of music. In my opinion, you should't care that much about labels, but you should care about the actual music. Otherwise, like Elvis Costello once said, that's just like "buying cereal and eating the box".
Independent musicians are only in the music game as they want to do something not just make money. They aren't tied down by what the label wants and can release music of any nature with any political message. They can also choose what gigs they play at not go to ones because they are told to.
I believe that independent musicians are generally better than those signed by record labels. Of course, I wouldn't say this is true of musicians who start out with another record label but then enjoy success to the point that they create their own label. In this way they receive the same independence, but with even more power and finances behind them.
Record labels are not interested in making great music, they are interested in what sells. This has much more to do with marketing, looks, and branding. Independent musicians can be so much more talented than those we hear on the radio, but without the right marketing, no one gets to hear them. Music should be about quality, not what sells.
Independent artists and musicians are far better than ones signed to record labels. Record labels, In my opinion, Make manufactured music. Record labels hire teams to compose, arrange and just about do everything except sing the actual song. Independent artists are far more talented. Music should be moving not manufactured or assembled by a team with a soul purpose to make money.
Once a musician is signed by a record label, the focus often changes from the music to the money the music can generate. More emphasis may be placed on making the music appeal to a larger group of people and subtle changes will be made in the music, in the musician's appearance, and in their interactions with the people around them. Independent musicians do not have to deal with the bureaucracy that record label musicians must deal with in order to keep their contracts. Independent musicians can focus on producing the music that is important to them, not to the record label. There are some excellent record label musicians (I listen to them every day), but most of them would probably admit that they have had to make concessions concerning their music in return for the record label contract.
I think that musicians signed by record labels are better than independent musicians, because musicians signed by record labels have more tools available to them to produce good music. Record labels also only sign people that they think will make them money, so the talent quality is likely to be higher.