Some time has passed since I looked through all these things, so everything could change in the last 3 or 4 months.
RDS is basically a pre-packaged version of MySQL on Amazon services. You do not need to worry about any configuration or server maintenance; they take care of all this for you. You can purchase / rent space / performance according to your needs, and you are provided with time guarantees from Amazon, and they take care of data security (i.e. replication, backup, etc.). However, I would recommend that you create your own dumps for your own backup purposes, unless you are ready to trust the Amazon cloud (I think it depends on what information you plan to store there)
EC2, on the other hand, is a virgin server with any operating system (they have pre-packaged devices with CentOS / Win available). Here you are on your own, no matter what you do. If you want to start MySQL, you need to install it, configure it, and save it yourself. If you need replicated data, you will need to create a second instance as a slave and confirm that the slave is synchronized. You could essentially install MySQL Enterprise if you want some of the benefits of Enterprise, but this is not required. The advantages of going along the EC2 route are that you have complete control over the database configuration, including any performance tuning you want to do. Alternatively, you can install a MySQL cluster if you need to. The disadvantage is that you must perform full system administration yourself, including OS maintenance, security, patches, etc.
There is also a difference in cost between the two. If you need to switch to a large database (disk space or performance), it is easier to make small incremental changes at the EC2 level than with RDS.
EC2 has recommendations for returning everything to S3 storage, since EC2 storage is not guaranteed in all cases. I do not remember where I read / saw this obscure information, but something that I always remembered. Thus, there is additional cost if you want to build a solid infrastructure.
In the end, it all comes down to the fact that you want to do it yourself and be responsible for everything except the hardware itself, or you want someone else to worry about all the software settings / backups / etc, but you just use DB .
Hope this helps.