When replacing fittings that had compression rings I have found it most reliable to cut off the old tubing with a tubing cutter near the old ring and then reassemble with new ring on a fresh tubing surface. This is usually feasible because the tubing is typically a flexible type and extra length is not a problem.
In some cases it is feasible to just replace the valve itself with the same type of valve and just reuse the previous compression ring and compression nut. But watch for leaks and be prepared to use the approach in the first paragraph instead.
For rigid tubing my preference is always to use copper and sweat soldered connections. These can be easily re-soldered if needed for replacements if the proper cleanup of the reused connection is done and proper flux is applied.