The key concept is always adherence to standards: if you plan to use 4D's custom and / or special designed functions (but the discussion could be far more general, and cover any other free or commercial tool in the wild), well, just use it and take your advantage.
Not surprisingly, that's why huge DB systems like Oracle or IBM's DB2 in the past were wide accepted for specific business areas, as commercial transactions, for instance.
The other main reason to adopt a very closed solution is the legacy support. One of the products you cited (Pervasive SQL) acted as a no-effort port for BTrieve-based applications in late 90s, and it gained popularity thanks to the huge BTrieve community all over the planet.
Finally, last but not least, you should evaluate the TCO (Total Cost of Ownership) not only in terms of license price (single seat, network environment, site licenses and so on), but also for what concerns tech support, updates and availability for your platform. Many business units I know have been obliged to change their base OS for DB related problems.
Tip: add a bonus for custom solution that are proven or supported for usage in virtualized environments, if you aren't in seek for extreme performances. It will save more than a head ache for your DB manager.
In all other cases, rely on opensource/freesoftware DBs. MySql and Postgres for big projects, SQLite for single app persistence layer. Fairly standard and very good (community) support. Good value for no price.