Well, there are more than half a dozen VPN options with Cisco... so sometimes its hard to know what is being used.
If there is no application popping up, it sounds like it is the Clientless SSL VPN solution. In this case, you are using SSL as your encryption type and the level is based on the SSL certificate used on the concentrator.
In your browser window, you should see the standard SSL padlock icon somewhere. (IE has it at the bottom, Firefox at the top right) If you double-click the padlock, the certificate properties will tell your your "Key Size" which is most likely 1024 or 2048... So your encryption level is typically below the key length, but it depends on several factors which are way out of the scope of this question.
But bottom line, unless you can get either: 1) the full AnyConnect client; 2) the IPSec client; or 3) the Java client w/ port tunneling setup, the answer is no. You will need to use the web unless one of the above criteria can be changed/setup by your VPN admin for you.
FYI... Windows file sharing over VPN is generally very slow. Your Internet and VPN latency matter completely in how fast your browsing will work. This may be why your admin is requiring that you use the web portal method.
Hope that help. -Cheers, Peter.
