Some advantages for me:
1. I don't touch your credit card or personal info. I don't want to know those things. I don't want to be responsible for keeping them secure.
2. Integration with the post office for generating shipping labels is seamless.
3. I think people are more confident to buy something from a little known business if they feel that PP is protecting them. The increase in sales probably covers the PP fee.
4. I can run my business from a passive web page. All of the other services require me to manage some kind of server, running code, that I become responsible for maintaining. I love coding, but don't want it to be part of this business.
From reading articles and forum posts two main sources of horror stories seem to be:
1. People who just seem to be "accident prone" in terms of getting into disputes with others.
2. Selling non-physical goods, which I can only imagine has its own pitfalls that I don't know about.