Mastic is the best and the most widely used duct sealing material. But mastic is messy to apply.
When to use duct tapes
Duct tapes tend to fail quickly and do not provide a permanent and elastic sealing.
But they can be useful to seal holes in the air handler and cabinets, or for temporary holding and bundling (e.g.: to maintain access for future service).
General guidelines when using duct tapes
The IECC code requires that all duct tapes used on duct board and flex duct meet the UL 181A/181B standards, but in practice that doesn't happen very much. Inspectors and contractors are not respecting it in many states, and the UL 181 standards alone are no guarantee of effectiveness.
Some contractors use butyl duct tape and OPP (Oriented Polypropylene) duct tape, which are much better than cloth duct tape.
You may consider OPP for sealing the flex duct to metal collars and the outer jacket of flex ducts. For manufacturers of these products, see: Intertape Polymer Group, Shurtape Technologies and Berry Plastics.
Butyl tape can also be a good choice, though relatively expensive. It can be used with galvanized duct, duct board and flex duct. For manufacturers, see: Hardcast.
Also do not forget, when selecting duct tapes: consider high quality tapes, avoid cloth-backed rubber-adhesive tapes, prefer OPP and butyl duct tapes or products qualified by the Underwriters Laboratories (UL).