One advantage of a character being part of a unit is that any Leadership tests the unit takes are then made using the character's Leadership value. If an independent character is part of a unit that falls back he may not leave the unit until it regroups. Independent characters never have to take 'all on your own' tests.
Errata — Chapter Approved: Main Rules Clarifications (v2.0): An Independent Character cannot leave a unit he joins, which subsequently falls back, until it regroups, and therefore if the group can't regroup, the character can't leave it!
Errata — Chapter Approved: Main Rules Clarifications (v2.0): If an Independent Character has joined a unit, which later falls back, and is subsequently eliminated (by shooting, for example), the character can then test for regrouping by himself.
Errata — Chapter Approved: Main Rules Clarifications (v2.0): If a unit is wiped out by shooting except for the character, he does not have to take a Morale check as if he were the last man as long as he is an Independent Character who only joined the unit. He then regroups without worrying about the rule for being in a unit below 50%.