I don't think this is a question of "reliability", it is simply that the two programs display different things. "Free space" sounds simple, but in reality it is quite complex - different people, different systems, etc. all consider "free space" to be different things.
For example "free space" could mean "how much of the disk space is not currently used for any meaningful data", or it could mean "how much more data can I store here" or something completely different.
The "About this Mac" tries to take the latter approach. If I add more things to this disk, how much can I really add. Technically it involves the calculation taking into account things that are temporary in nature. Often the largest differences here comes from local TimeMachine snapshots (they're created on the source volume, not the backup disk). These are temporary and will be removed automatically.
In contrast, df takes a very "technical" approach and shows the "raw" file system information according to how much of the disk space isn't used for anything meaningful. I.e. even for example temporary TimeMachine snapshots are included in "used" as they're actually storing useful data.