FileZilla FTP to AWS EC2 Windows Server 2012 Instance: Failed to retrieve directory listing

While you have opened port 14747 on EC2 firewall, supposedly for a passive data channel, your server listens on different ports and mainly on wide port range, not on a single port.

From the client log:

Response: 227 Entering Passive Mode (172,31,34,244,202,201)

Where 202*256+201 = port 51913

From the server log:

(000004)9/14/2014 9:02:45 AM - administrator (31.16.50.63)> 227 Entering Passive Mode (172,31,34,244,202,205)

Where 202*256+205 = port 51917

I assume that you have not configured the server to use the port that you have opened. Use Passive Mode Settings in FileZilla Server Options:
https://wiki.filezilla-project.org/Network_Configuration#Passive_mode_2

Note that using a single data port might cause problems, if you do not guarantee that the port number is reserved for the server.
See How many data channel ports do I need for an FTP server?

Also you should configure the FTP server with its correct external IP address.

Response: 227 Entering Passive Mode (172,31,34,244,202,201)
Status: Server sent passive reply with unroutable address. Using server address instead.

While FileZilla client (and other FTP clients) can handle server returning invalid IP address, some FTP clients (rightfully) do not. See External Server IP Address for passive mode transfers on the same options page.