Yes, you still have a job. But you also have the knowledge that (even though it probably wasn't your fault), you just turned someone else's life upside-down, and you have no power to do anything about that. The person who was fired will probably get resolution in the form of a job somewhere else, but you'll rarely ever get to share in that resolution.

To clarify, the person losing their job has the bigger problem and are worse off. But the person doing the firing pays a cost as well, and between the two, getting fired is easier for me to handle than firing someone.

Layoffs are probably a little different because they're less personal, but I've not experienced those, so I don't know.