Casing extraction during bored piling works.

In most cases, I would prefer method (b).

The vibro hammer is used until the temporary casing is sufficiently loosened from the surrounding soil. Once the casing is effectively free, the casing can be supported by the crane, the vibro hammer can be released, and the casing can then be lifted and laid down using the crane and appropriate rigging.

Lowering a large 1.2 m+ casing horizontally while it is still clamped to the vibro hammer is possible in some situations, but it adds unnecessary handling load to the hammer and clamp and can make positioning and disconnection more difficult. There is also a greater risk of damaging the hammer, clamp or casing during laydown.

There are exceptions. If the excavation is unstable and the casing must be removed quickly, or if the contractor's equipment and method statement are specifically designed for combined handling, the casing may remain attached to the vibro for longer.

For long or heavy casings, particularly where casing sections must be disconnected, using a separate crane line or lifting arrangement for the casing is generally the better-controlled method.

The exact procedure should ultimately follow the vibro hammer manufacturer's lifting limitations, the crane lift plan, casing weight and the project's approved method statement.

For general technical information on hydraulic vibratory hammers and pile-driving applications, this reference may also be useful:
https://www.powerquip.co.kr/news/us-vibratory-hammer/