1. Your operational overhead will increase _a lot_. Be ready to hire on a lot of ops staff if you expect them to do anything but put out fires. And as you grow you'll need experts, people like network engineers.
2. Any weirdness you experienced with AWS infrastructure will be replaced with weirdness in your own environment, except now you're on the line to troubleshoot and fix it yourself.
3. Operation staff will immediately start guarding the food bowl as resources become finite. Server provision waits start to seem like breadlines. Power is consolidated with Those Whom You Must Ask.
4. Your cost will decrease, sometimes significantly so.
5. You'll have more hardware flexibility to run your app just the way you want to (Stack Overflow's mega databases come to mind[0]).
In the end I think this type of transition is for stable companies that don't mind or even prefer strong divisions of labor (coders who code, sysadmins who sysadmin, testers who test), but it's not for startups or companies that hope to move with any kind of strong velocity.
[0] http://highscalability.com/blog/2014/7/21/stackoverflow-upda...