VIX APIs and VI APIs cater to different needs. VIX is primarily meant for automation. Its an API that lets you programmatically control the products that host VMware VMs, and control the VMs themselves. If you're considering learning more about the VIX API, chances are it's because you need some form of automation. Its a complement to the VI API
The other difference is that bindings for VIX are provided for C,Perl and COM
The type of operations similar to VI APIs include Connect to a host, register, unregister vms, power off or power on a vm. The operations that are not possible through VI APIs or VI SDK but are available through VIX : installing vmware tools in a vm, vm guest operations e.g. copying file from host to guest, allows to copy files in and out of guests and allows you to start and stop processes within guests
On the other hand, VI APIs let one manage the inventory, manage vms, hosts, configure networks, monitor performance data, manage tasks, alarms, migrate vms, get updates on properties etc.