I find the new file comparison feature very good and useful and would like to use it with external tools such as TortoiseGit.
Is there a way of invoking this feature from an external application?
Could not find any info either here or in the documentation.

Have a look at SmartGit www.syntevo.com/smartgit/features.html

It is free for non-commercial use and it has lots of great features, including a good differences/merge capability.