What basses are considered flat tops and curved tops and are there any advantages to either one?

It easier to see this on guitars:

A 'flat top' instrument is like your Jazz copy: The face of the instrument (where the pickups, knobs, pickguard and bridge are mounted) is flat, just like a Telecaster or Stratocaster. A Kahler install on this is what they are talking about. Your bass is good to go for this.

A 'carved' top (which is what I believe you mean, instead of curved) has a rise in the middle where the bridge and pickups are installed, like a Les Paul guitar. Putting any kind of wiggle stick on one of those can be relatively simple on the bridge and stop tailpiece mounts, or can run into countersinking major surgery. There are relatively few carved top electric basses.