What RDBMS are you refering to ? MS SQL Server does not have "Incremental backup". It just have full, differential and transaction Log backups.
You can equate (loosly) transaction Log backups as Incremental backup as it will require a FULL backup and all the increments (which are nothing but
transaction backups) until the point-in-time failure.
Differential backup works differently, as you only need a FULL backup and the last differential backup and the database can be brought to the point
when the differential backup was taken. After that you have to restore T-log backups, so that a point-in-time recovery can be performed.
Considering above facts, most DBA's or server admins prefer Full backups and subsequent Incremetal backup (T-log backups) to
a. conserve disk space
b. Time required will be less as compared to restoring a FULL backup.
Note that, the recovery model (e.g. BULK LOGGED, SIMPLE, FULL) also plays important role when you go for T-log backups (Obvisously, SIMPLE recovery
is out of picture when it comes to taking T-log backups).
The only problem with Incremental (T-log) backups is that if you loose any of those, the database can only be restored to the last unbroken log chain.
Imagine someone deleting files, etc. Also managing them is an extra overhead as well.