Something like this perhaps?

Two files, A1 and A2.

$ sdiff -B -b -s A1 A2 | wc would give you how many lines differed. wc gives total, just divide.

The -b and -B are to ignore blanks and blank lines, and -s says to suppress the common lines.

https://superuser.com/questions/347560/is-there-a-tool-to-measure-file-difference-percentage has a neat solution for this,

wdiff -s file1.txt file2.txt

more options see man wdiff.