The core difference
Off-the-shelf software is designed for a broad market, while custom software is designed around a specific organisation. The important question is not which category is universally better, but how closely the technology needs to fit the workflow.
When packaged software can work
Packaged products can be useful when the organisation's process already fits the product, integrations are available and the expected changes are limited.
When custom development becomes useful
Custom development becomes relevant when workflows are distinctive, multiple systems need to connect, information needs are specialised or the organisation needs control over future product changes.
Questions to ask before choosing
Map the current workflow, required integrations, data ownership, reporting needs, security requirements, expected changes and total operating cost. These questions create a better decision basis than comparing feature lists alone.