Using wdiff:
$ wdiff -3 a.txt b.txt
======================================================================
[-b-] {+B+}
======================================================================
The -3 or ---no-common option will remove words that are common between the two files and only show the differences.
The ===... banner (and empty lines) may be removed with grep:
$ wdiff -3 a.txt b.txt | grep -vx '=*'
[-b-] {+B+}
wdiff may also read unified diff data if you give it the -d or --diff-input option, for example from git:
git diff somefile | wdiff -d -3
Although wdiff is not a POSIX tool, it is commonly available.