I have ran a small site of my computer (only have one and I use that for other things as well), windows system. ADSL connection, round 1mb up speed.
I found it fairly easy to set up with mysql and php. Never got apache to work though so I did chose abyss webserver (free for use in the light version, which can not do separate domains).
The problem I ran into that made me go hunting for a host was the fact that during bad weather (thunder storms) I often had to turn the computer off to avoid risking a fried computer, if there's an electricity outage, the site is not accessible. If for some reason router and/or ISP had problems the site went offline.
Simply I chose a hosted solution to get better stability, and faster connections. At that time I did host a clan forum for a travian clan where the users came from various places around the world, they wanted access at all times naturally.
Yes, for the most you can control the uptime, and yes it is by far easier when it comes to editing your site, as there's no upload step involved. And yes, you can control the php config completely which give you greater freedom.
Note that you also need to deal with securing your web server, I learned that the hard way, luckily they did no harm other then screw my site up.
I didn't notice any change in electricity cost, although that could be because nothing really did change, computer has always been on more or less 24/7.
In the end I did find a hosted solution more reliable. I still have a local server setup for testing, and could if needed make it available and point my domain(s) to it with information if the server would fail.