Response: 227 Entering Passive Mode (192,168,1,78,5,245)
Status: Server sent passive reply with unroutable address. Using server address instead.
It looks like the server is inside a private network, that is behind a router/firewall. But you access the server from outside the private network. Unless the router/firewall has special helpers to deal with this situation and to rewrite the traffic this will not work with passive mode. Given the above response from the server received by the client you have no such router/firewall.
In this case you would have to need active mode. But, if both client and server are behind such a router/firewall and are in different networks even active mode will not work.
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.
Best Answer
While this question is old, there's no really comprehensive answer. So I'm adding one.
In the passive FTP mode (the most common mode nowadays), the FTP server listens on port 21 for an FTP control connection. But for all data transfers, including directory listings, it listens on an additional port. The port is picked out of a configured port range.
If you open only the 21 control port on the firewall, you get the described behavior. You can connect, but you cannot list directories or transfer files.
For details, see my article on Network configuration for passive FTP mode.
You have to go to Control Panel > System and Security > Windows Firewall > Advanced Settings > Inbound Rules > New Rule and add a new inbound rule for data port range your FTP server is using.
The port range that the FileZilla FTP server is using, is configured in Edit > Settings > Passive mode settings > Use custom port rage. You can configure a narrow range (like 10 ports), to limit a number of opened ports. You should use port numbers 1024 and above (up to 65535).