In Florida, it is partial public record. Similar to driver's licenses, much is available, but some important details are left out except for other law enforcement agencies. However this is in a state of flux as there are suits and countersuits to shield from view, and expose more.
Interestingly (and, why should it surprise me), some jurisdictions in California use the public record aspect to discourage applicants. I had inquired about a carry permit, that is, a jurisdiction's policy, a few weeks ago. The short story is that the wife wants CA, I don't, but you know how that can go. Anyway, I got an e-mail back from an administrator who said , among other things, that "there is a great deal of personal information that is made public record." It was certainly done in a discouraging tone, indeed somewhat snotty as the letter went on. As explanation for that they went through the background check "with fingerprints" etc. (as if that were something unusual or a big deal) and concluded with "As you can see, it is very difficult to get a handgun carry permit in California. I wanted to write back, in an even, though cold, tone that the requirements are the same in FL except for the personal references and the "reason". (We are "shall-issue.") The CA characters seemed to be trying to imply, without saying it outright that we just hand out permits, which is untrue. Anyway, I don't mean to digress, just going into a context in which the CCW files are stated to be public record, and such use was partially as a discouragement.