cmp does things byte-by-byte, so it probably won't run out of memory (just tested it on two 7 GB files) -- but you might be looking for more detail than a list of "files X and Y differ at byte x, line y". If the similarities of your files are offset (e.g. file Y has an identical block of text, but not at the same location), you can pass offsets to cmp; you could probably turn it into a resynchronizing compare with a small script.

Aside: In case anyone else lands here when looking for a way to confirm that two directory structures (containing very large files) are identical:

diff -r --brief will work and not run out of memory.

cmp does things byte-by-byte, so it probably won't run out of memory (just tested it on two 7 GB files) -- but you might be looking for more detail than a list of "files X and Y differ at byte x, line y". If the similarities of your files are offset (e.g., file Y has an identical block of text, but not at the same location), you can pass offsets to cmp; you could probably turn it into a resynchronizing compare with a small script.

Aside: In case anyone else lands here when looking for a way to confirm that two directory structures (containing very large files) are identical: diff --recursive --brief (or diff -r -q for short, or maybe even diff -rq) will work and not run out of memory.