Regarding Cisco AnyConnect Secure Mobility Client and its compatibility with Linux these are the Release Notes where further details can be found. As far as version 4.10 (2) of VPN-Client is concerned it is low number of distributions: few Red Hat releases as well as few Ubuntu releases. Freedom of choice is quite small.
in practice the facts can however deviate from statements made on paper.
Which distributions proved so far to provide good, stable compatibility with Cisco AnyConnect Client?
(2) My role is workstation user working remotely and connecting to network using exactly this client, network of organization I am member of and working for. I can administer only that one workstation. Network IT provides so far only release 4.10 of client. From standpoint it is unknown if organization will ever upgrade to newer releases. Yet, should it happen - how soon will that day come.