man of watch says
watch - execute a program periodically, showing output fullscreen
where
-n, --interval seconds
Specify update interval. The command will not allow quicker
than 0.1 second interval, in which the smaller values are con‐
verted. Both '.' and ',' work for any locales.
-d, --differences [permanent]
Highlight the differences between successive updates. Option
will read optional argument that changes highlight to be perma‐
nent, allowing to see what has changed at least once since
first iteration.
-t, --no-title
Turn off the header showing the interval, command, and current
time at the top of the display, as well as the following blank
line.
man of cat says
cat - concatenate files and print on the standard output
man of tee says
tee - read from standard input and write to standard output and files
This might work
Watch for differences between 2 version of doc.txt every 10 seconds and write it to a file doc.txt
watch -t -d doc.txt -n 10 | tee new.txt