We are all happy about the new web Client for Lync 2013. No more SilverLight is needed to run this Client.
But if you still run Your Windows XP (not supported any more from Microsoft), be aware that you will not get this in Your Web Client:
On supported Windows XP, Windows Vista, and Windows Server 2008 operating systems, computer-based voice and video are not available. Application viewing, application sharing, desktop viewing, and desktop sharing are available.
This has nothing to do With Your browser but Your operating systems. You need to get your IT-Department to Upgrade to a more modern OS.
More information about what kind of functionality you will get in your web Client when installing the plugin you can read about here