Firstly, when you talk about a shared hosting plan I assume you don't need to set up the server, you just drop your files in the htdocs folder and your site is ready to go. EC2 instances are analogous to a vps system. You're responsible for setting up the operating system, installing apache, php and mysql. There are 'images' (not sure that's the correct term) set up with everything ready to go but that still leaves you responsible for a lot more of your site than you may be currently.
My understanding is that MySQL is problematic. Currently each instance is given a certain amount of hard drive space but if that instance crashes for any reason all the data is lost. The intention is that S3 is used for your permanent storage but it isn't suitable for running a database on. Permanent drives have been announced but they will only be available later in the year. Until then you are left with work-a-rounds, frequent backups to S3, mirroring drives across instances in the hopes that you'll only ever lose one instance.
Connecting multiple web servers to a single backend database server is handled in the same way it would be with any other vps service or indeed dedicated servers.