I owned the diskette version of Privateer and been thinking about buying the CD release back then. But had no money as a kid.
The main differences to the original diskette releases were a) the additional missions/story from the Righteous Fire expansion already there and b) extended speech, beyond the Speech Pack diskette release. Basically, all on one CD plus extras.
Hope this helps solving the confusion.
Usually the diskette speech packs only added in-flight talk and a few lines (e.g. in Wing Commander II intro), the CD medium offered more space so all text lines were done by voice actors.
If I recall correctly the re-recording was done because the original voice actors from the diskette release weren't available. It would've been odd for the voices to change in the game, so all dialogue/text lines were re-recorded.
Indeed, compared by today's standard the sound quality is low, but was pretty good for 1993+.