Heroku and Engine Yard uses Amazon EC2. That's where the similarities stop, though.
Heroku has a very special setup where you don't have write access to the file system. They do that in order to be able to scale easily with their setup, prompting users to use HTTP caching (varnish), S3 and the likes, instead of serving dynamic content via the file system.
Engine Yard has a pretty standard virtual host-ish setup, where you have write access to the file system.
So, the answer to your question is: no, there are no problems or special cases you have to worry about.