I'll open. Since the obvious debate is Rebecca vs. Louise, I'm putting my FFXIII comments in a spoiler rather than have you sift through them. Don't respond to the FF part yet, I'm still working on it. Current done Chapter 3 (in my opener). Rebecca v. Louise is good to go, though.
Ah Rebecca. A young girl who gets spat on thanks to her being the best of the worst (archers and snipers). It's quite sad, really. Especially when she's a better archer than the Countess of Reglay.
Anyway, Rebecca starts out in Birds of a Feather with the rest of the Pherae army. I guess it helps when the game tosses Peg Knights your way in her first chapter, eh? She's got great availability and she's great for taking out Peg Knight nuisances so that your axemen (Bartre, Dorcas, Hector) can concentrate on the real threats, the Brigands.
Point is that Rebecca has fantastic availability when comparing her to Louise. Becky arrives on the first turn of the second chapter of HHM. Louise joins the party about twenty chapters later. Points given to Becky for existing and helping the team.
What's that, you say? Rebecca is an archer and is automatically terrible? No enemy phase? Well, y'all can go stick your dicks in a rotary blade. While Rebecca might be stuck in a bad class with mediocre starting stats, she has quite a few perks. Let's take a look, shall we?
1. Longbow usage. 2-3 range weapon? Yes please. This weapon immediately makes archers better since the first one drops pretty early in the game (I'd love to say around Chapter 17 but don't quote me on that one). Hitting targets 3 spaces away gives her an advantage over everyone for a chapter like Genesis. And if I need to spell it out for you why it's so good, you haven't played the game in a long time.
2. Her growths. While Rebecca's bases might be pretty frail, she makes up for it in growths. Her Str sits at 40, rivaling units like Kent and Florina who are known for their reliability in combat. Her 60 Spd growth is only topped by Matthew, Guy and Ninils while tying Lyn, Nino, Legault and Dart, making her one of the fastest characters in the game. 50 Skl and 50 Luck just add to her potential to become a dodge tank.
3. Competition or lack of for a promotion item. Yeah, that's right. Assuming that you use Rebecca (why wouldn't you?), she's an absolute shoo-in for the Orion's Bolt. Wil is statistically inferior to her and Rath comes too late to use it effectively, even with an early promotion. If you're trying to S Rank HHM, Rebecca's the way to go for an archer.
4. Effectiveness on flying units. While Peg Knights pretty much suck and can be taken down by almost any unit, Wyvern Riders are actually tough enemies to fight. In New Resolve, WK's fly out of the darkness with their 28-31 HP and 10-11 Def. But since Rebecca can deal effective damage on them, she hits them for about 22 damage with an Iron Bow at level 13, setting up a kill for a much weaker unit. Now tell me that being an archer sucks.
So Rebecca fights and grows and is given a lovely Orion's Bolt as a birthday present. She then uses it in the Unfulfilled Heart base, promoting into a Sniper. And on the very first turn, Mr. and Mrs. Reglay show up...
Rebecca - Level 1 Sniper - A Bow - C Lowen, B Dart
Iron Bow: 24 Atk, 18 AS, 136 Hit, 22 Crit, 64 Avo, 13 CEva
Steel Bow: 27 Atk, 15 AS, 121 Hit, 22 Crit, 58 Avo, 13 CEva
Longbow: 23 Atk, 14 AS, 116 Hit, 22 Crit, 56 Avo, 13 CEva
Killer Bow: 27 Atk, 17 AS, 126 Hit, 59 Crit, 62 Avo, 13 CEva
32 HP, 8 Def, 9 Res
Louise - Level 4 Sniper - A Bow - A Pent
Silver Bow: 26 Atk, 17 AS, 126 Hit, 14 Crit, 57 Avo, 20 CEva
28 HP, 12 Def, 15 Res
Man, I wish I was making these numbers up. Becky is destroying Louise offensively and only loses badly on the defensive side when Louise is near her husband. Playing Lowen and Dart (both great units especially if you're not trying to S Rank) knocks Rebecca's Atk, Crit and Avo right up thanks to both supports being FirexFire (best support in the game IMO) along with being decently quick (Lowen is 5 +2 but starts in Chapter 12 while Dart is 35 +3 and hits C after only 15 turns). And Rebecca's destroying Louise when Countess Reglay has the better bow.
At this point onwards, Rebecca begins destroying Louise. Her growths are much better, she's got better supports (IcexLight isn't bad but it's not great) and is better at dodging attacks if someone tries to go after her. If Rebecca beats Louise in Louise's joining chapter and has more room than Louise to grow aside from having more potential, it stands to reason that Rebecca > Louise for when Louise exists and Rebecca > Nothing when Louise = Nothing before Unfulfilled Heart.
I rest that case.