I do both. Most of my own hosted sites are now mirrored in WordPress.com, so if one goes wrong I can redirect from my control panel. The advantages of both are thus:
Any security issues are theirs and not yours. Having a domain banned by my hosts recently because it was spamming, unknown to me was a wake up call. My host said it was the WP at fault. Others here said it was the server security.
Now I am proficient in lot's of things but life is too short to learn php scripting. If you want to know about machinima and all it's technicalities ask me. I run a forum on that subject.
The other point is that the script doesn't go wrong and if it did it wouldn't be upto you to fix it. The help forum is not inundated as this one - presumably because fewer things go wrong - which means you will more likely get the answers you want.
When you host your own WP you have a large number of plugins/widgets available, whereas there are not that many on WP.com
If you have any problems with your install - and there can be plenty, you may not get any help and your thread will have gone into the abyss within hours. It's a no win situation because if you "bump" your thread it may well be ignored.