Is it possible to use BeyondCompare for comparision in "Local History"?

No, this is not possible.
What are you missing in the built-in history view?

View of differences in BeyondCompar is neatly arranged.

See attachments.

OK, I suggest, then, filing a request for improvements of our Diff view.
Please describe what you would like to have and attach the screenshots.

Thanks, done.

http://youtrack.jetbrains.com/issue/WI-12114