First of all, the reason Final Draft does it that way seems to be that since it adds it as part of the Character element (i.e., after the character name, as if you'd typed it) then it has to necessarily assume the same formatting as the Character element. Since the Characer element is typically all-caps, the (CONT'D) text has to be, too.
So it's really a what's-easiest-for-the-software explanation.
Note that it didn't used to be this way. Before screenwriting software, it used to be a separate line below the character name, like:
And here is where I have more
But that's a little harder for software to do automatically.
Fade in attempts to split the difference. Because it automatically adds the (cont'd) in a different manner, it's not required to retain the same formatting as the Character element style and therefore doesn't need to be forced to uppercase. The result is intended to be more discreet and unintrusive than the all-caps (CONT'D).
At any rate, if you'd like to change it, you can easily do so under Document > More and Continued.Tags: cont'd, continued