One of the important difference is that during the time VACUUM FULL is operating on a relation, no other operations will be allowed on that relation. Most of admin care about this point, because they don't want to stop operations for background garbage collect.
While that is true, it is not a reason not to update pg_stat_get_last_vacuum_time.
I'm having a hard time coming up with a reason not to update pg_stat_get_last_vacuum_time with a full vacuum.
On version 8.4 and below, you could justify it by saying that VACUUM FULL bloated the indexes and then left them that way, and so we shouldn't update the time field. But that is no longer the case. And even then, doing a ordinary vacuum afterwards isn't going to fix the index bloat, so even that argument is a bit sketchy.