The older AnyConnect client software did not include as many optional modules (Network Access, ISE Posture, etc.) as the new AnyConnect Secure Mobility Client.
Even if you're only using the VPN module, the later versions also patch lots of bugs (including security-related ones) and add support for the latest OS versions.
Note that moving from version 3.x to 4.x requires a (no cost) migration license. Assuming you have support on your ASA, you are entitled to run the latest 3.x images without a migration license.