Both deliver millimetre precision, but excel in different situations. A practical comparison.
The automated total station and GNSS are the two workhorses of geodetic monitoring. They are not mutually exclusive — they often complement each other — but the choice depends on the site.
The total station
A total station measures angles and distances to prisms and achieves the highest relative precision (sub-millimetre). It does require a clear line of sight, and performs best over shorter distances within a single site.
GNSS
GNSS measures absolute position via satellites and needs no mutual line of sight. This makes it indispensable on extensive or fragmented sites, but precision is slightly lower and it requires a clear view of the sky.
In practice: combine
In practice we often combine both: GNSS for stable reference points over large distances, and a total station for fine measurements within the site. This way you exploit the strengths of each technique.