Firefox ESR is an older version of Firefox that continues to receive security updates. It is made for conservative enterprise environments that care more about stability (as in: not changing) than features or fixes. It may or may not be more stable (ideally, newer versions would fix stability issues in older ESR versions), and may use more or less memory (regressions in memory usage should be reported).
I have tried it in the sense that I have a copy around for testing in those odd cases where someone is using ESR. I don't recommend it.