Hydrotest can be as high as 100bar, pneumatic only up to 2bar.

Well hydrotest is preferred over pneumatic testing due to a couple of reasons etc specification and equipment limitations or sometimes design limitations.

Some specs allow pneumatic testing only up to 2bars. To find out why you need to do your own research.
It is actually quite hard to maintain\hold air pressure.

Hydrotest can be above 100 bar on certain hydraulic lines. You will see this depending on projects you work on. Pneumatic testing can go way above 2 bar but refer to the limitations above.

Application, cost, maintenance will determine which is the best.
http://www.chemkb.com/equipments/heat-exch...exchanger-pche/
There's no direct right answer on this. Like a crude oil refinery, normal shell and tube exchanger will do the job.