Good question! I'd say the following things:

• Almost all shared hosting uses proprietary software as the basis of making its stuff "easy"; almost certainly cpanel or something cpanel-like that's nonfree.
• A lot of this is parallel to old hacker complaints about being stuck as a single user on a time-sharing operating system. If you're lacking root, you're lacking a lot of power.
• Daemons such as XMPP/SVN/etc daemons, etc are usually prohibited, or made very difficult to run, or require special permission.
• Trying to get anything that's not PHP on shared hosting is usually pretty tricky.
• Trying to get system packages on shared hosting... well, you have to pray for the best. The saddest MediaGoblin installs have been those where people have been trying to compile the entire gstreamer stack by hand. not pretty!
• "jailshells"
• Large set of constraints... constraints aren't necessarily bad, sometimes constraints can be liberating. Totally unconvinced that shared hosting constraints match that though.

I may have more things, but that's it for now :)