I use Crossfire. I tried Crossword Compiler once, a few years ago. It does one thing Crossfire doesn't do--it creates (or tries to create) a grid for you if you enter your grid constraints and theme answers. Maybe this is useful for new constructors, since designing a grid is the least intuitive part of crossword-making; it's not at all useful if you're in the habit of designing a grid to fit the demands of your particular theme set.
Otherwise, the main thing Crossword Compiler does that Crossfire doesn't do is take your money year after year. Crossfire costs $50-you pay it, and that's that. Crossword Compiler costs 2, or 6, or 25 dollars a month, forever. And if you have a Mac, as I do, you have also to pay for an emulator to run the thing (Parallels costs $99/year), and for Windows itself (Windows 11 is $139).
If there are other advantages to Crossword Compiler that justify such an outlay, I too would be interested in hearing about them.
David Alfred Bywaters