The main difference in MKVIe is Remote I/O. Instead of device I/O coming over analog connections to the MKVI panel to process, a remote I/O module is installed near to the device(es) and the signals are sent to the Control System over Ethernet. This means fewer cables between the turbine and the control system, easier commissioning and better communications.
How much is different depends a lot on your industry. The Mark VI was largely used for power generation applications and turbomachinery. The Mark VIe is geared for DCS and even some general market applications, particularly where safety systems are needed. The general philosophy (or terminal boards) for turbine control didn't change much in the Mark VIe, one of the reasons for not calling it a Mark VII. The design of the control hardware, firmware, and engineering tools is quite different. You can google "Mark VI versus Mark VIe" and get a PDF from GE that summarizes the differences from a turbine control perspective.
The Mark VIe makes a fairly good DCS platform, whereas the Mark VI had a lot more limitations. In particular, an entire plant is often controlled by Mark VIe, particularly using smart I/O like Foundation Fieldbus. The smaller form-factor has also allowed the Mark VIe to be used in applications like wind turbines and small aeroderivative turbines. Most recently, the Mark VIe sports a hypervisor that allows the realtime control to co-exist with Predix edge applications managed from the cloud.
If you search for Mark VIe on control.com you can find many, many more details. However, take answers with a grain of salt, as much of the posts are very old or are dealing with people's recollections of old versions of the Mark VIe platform. It has been constantly improving for over 16 years.