A lot of changes were made from "The Cage" to "Where No Man Has Gone Before." The only holdover from "The Cage" was Spock. (Majel Barrett would later appear in "The Naked Time" as Nurse Chapel) Jeffrey Hunter, who played Captain Pike in "The Cage," quit Star Trek because the producers and directors weren't willing to cooperate with his demanding wife.
Also, as you may or may not know "The Cage" footage was later reused in the two part episode, "The Menagerie."
A few of ther things I'd like to mention about "The Cage" include the weird way that the Enterprise goes into warp speed. (The viewscreen fades in and out)
The hand phasers used in "The Cage" were also used in "Where No Man Has Gone Before" and "The Man Trap." The same goes with the communicators.