I'm going to start with motivation. I would say that if you are going to self teach, you need bundles of motivation, because you are going to have to keep yourself motivated throughout this entire process. If you have a teacher, you feel more motivated to practise because you have someone to impressand someone who wants you to do well. If you don't practice, you don't progress.
Another factor is money. If you are going to be taught, usually you will have to pay for your tuition. I pay £10 for a half hour piano lesson. Other people will pay more for tuition, others lessons. Whereas if you self teach, you don't need to pay anything to learn, although you will need to buy an instrument.
When you teach yourself you can play whatever you like, but with a teacher, you tend to follow a specific set of books. Personally, when it comes to this I think being taught is better, because the skills you learn from the books the assign you teach you skills that are transferrable to other songs. They are usually teaching you necessary technique.
Overall, I would say that I prefer learning with a teacher, but what do you think? Would you prefer to teach yourself? Is paying for lessons over rated? Let me know In the comments.