It’s credited as being based on the Frederic Brown story Arena, but it wasn’t consciously based on that story. Somebody noticed that the script resembled it, so they decided they’d better be smart and secure the rights. The identical titles weren’t a coincidence, they only chose those after branding it as an adaptation.

Nothing deserves to be compared to The Alternative Factor.

I think the only interesting difference between The Cage and The Menagerie is the ending.