Here is few differences.
AJAX IE Client Plug in 1. No extra download and Installation required. Good for Chrome, firefox and safari 1.IE plug-in is required 2. Direct tunneling, much faster over HTTPs 2. Faster in selections, depend upon the configuration 3. Good for Mobile Device 3. Feature is not available 4. Requires ports 4747 and 477e open in both client and the server both inbound and outbound 4.This is done over HTTPs. So no port issue. 443 is usually open. 5.MS Office Integration is difficult 5.Microsoft Office drag and drop only available in IE plug in 6.Macro and alert is not possible 6.Alerts can only be created and triggered from Windows (IE Plug-in) versions of QlikView 7. The communication between a QlikView Server and a QlikView Windows client is encrypted. If, however, the AJAX client is used, the communication is not encrypted
As far as the network configuration is concerned, there may be a big difference: AJAX always communicates to a Web Server (either QVWS or IIS). Plugin acepts qvp:// pseudo URLs, so the communication is done directly between the QVS and the Client. This method is considerably faster, but requires ports 4747 and 4774 opened in both client and server both inbound and outbound.
When port 4747 is not accesible by the Plugin client, the server falls back to HTTP tunneling (port 80). This will degrade performance, because security packets are transferred and the network traffic and the use of bandwidth increases. Communication in this case is always between Client and WebServer on one side and WebServer and Server on the other.
I'd say that the biggest advantage of AJAX client is that it doesn't require any installation on the client's side, but it may require some design tuning.
It's up to you to choose one option or the other, avoiding tunneling when possible. In short, Plugin requires software installation client side, but rendering is WYSIWYG. AJAX doesn't need any installation other than a browser, but it may lack some design options.