Sufficiently ADJ that here works in the same way as so ADJ that or sufficiently ... [for SUBJ] to in order to what degree of 'difference' functions exhibit.
Functions are sufficiently different (from objects) that they have ... =
Functions are so different (from objects) that they have ... =
Functions are sufficiently different (from objects) to have ... =
If you say that they are sufficiently different in that you are saying something quite different: that functions are different enough to satisfy some need (which, presumably, has already been described). The in that clause describes some qualification or alternative description of that sufficiency; in this case it would a description of how they are sufficient, to wit, by having their own return values. In paraphrase:
Functions are different enough (from objects) to meet our need, because they have their own values.