Direct answer
Pneumatic tubes can be extremely fast for suitable small payloads between fixed stations; robots handle a wider range of containers and routes without installing a full tube network.
Where pneumatic tubes excel
They can provide rapid point-to-point movement for compatible payloads where stations and infrastructure already exist.
Where robots excel
AMRs can carry larger or diverse items, adapt routes, serve multiple hand-off points and avoid some fixed infrastructure.
Hybrid strategy
Many hospitals can use tubes for suitable urgent samples and robots for larger, sensitive or mixed logistics tasks.