I would think a major limitation would be not being able to host anything else but your one wordpress site for 20 bucks/mo. You couldn't have separate websites like on shared hosting or vps. I doubt you could use multisite due to the nature of the service, you are only allowed one wordpress site unless you pay for more. With shared hosting you do not update php, mysql, etc. I can't speak about mysql since I never tried to see if it was possible but I have installed a different version of php under my shared hosting account before so I'm assuming it's still possible. Eventually DH gets around to upgrading to a stable releases of php and mysql.
IMO, unless you have an existing WP site that has a lot of traffic I would go with shared hosting or vps. If you have a popular WP site and you don't plan on having anything else, DreamPress might be worth it. Otherwise, shared hosting would be fine if you are just starting out and you might consider vps later.