1. hardware you own is in a separate legal category, and it's somewhat harder for j. random people to subpoena the contents of hard drives you own as opposed to ones you rent.
2. It's harder to exercise due diligence and appropriate care on machines whose very existence is hypothetical to you.
3. you can do things with hardware that are difficult if not impossible to do on commodity VPSen. Like dropping a couple of Cavium cards into a machine that's going to be doing high-volume row level cryptography in a transactional db. Tuning disk arrays for maximal performance, etc.
4. Audit controls are easier to implement if you control the datacenter.
All that said; if you aren't dealing with sensitive data and don't have any potential dependencies on special hardware, and are willing to live with the fact that anything you do out in the cloud is potentially visible to outside scrutiny and interference; go for it.