Oscar vs. JillAssumptions:
Jill's optimal resource bundle is ~1000 Bexp sometime before C15, the C13 Speedwings if her Speed is lagging, and the C12 Seraph Robe if she needs the extra durability, and perhaps the C12 Arms Scroll for A Axes. Jill will use the Full Guard when there are Ballistae that threaten her. Jill might also be the best candidate for the Boots. Then again, she might not (especially if Marcia is recruited and trained). Jill's contributions will be considered with and without the Boots.
Nature of the Argument:Deployment: When considering Jill's contributions, I will consider playthroughs where Marcia is and is not used. When considering Oscar's contributions, I will consider all four possibilities of using and not using Marcia and Jill. Otherwise, nearly optimal deployment will be assumed, but only as a simplifying factor. If ever Jill or Oscar have a comparative advantage when the assumption of optimal deployment is lifted, I will try to point it out. If I have been less than vigilant in my efforts here, I encourage others to step in.
Resources: Measuring opportunity costs is a challenging feat. I will work around the need to do so by crafting an argument in Jill's favor. I will assume that Jill receives her optimal resource bundle. I will, with minor substitutions mentioned later, assume that Oscar receives Jill's optimal resource bundle. These assumptions most favor Jill, because she receives her optimal resource bundle, whereas Oscar receives resources that may or may not be optimal for him. See
this post (and those that follow it) for an explanation of the validity and rigor of this technique.
So, Oscar will receive ~1000 Bexp sometime before C15 (same as Jill). Oscar will receive the Speedwings, Seraph Robe, and Arms Scroll if Jill does. Because Oscar will have a commanding level lead when Jill is recruited and get the same amount of Bexp, Oscar will retain a level lead over Jill throughout the entire game. Oscar and Jill's Atk will be very similar, Oscar will have a slight concrete durability advantage, and Oscar will have a noticeable Spd advantage. In this argument, Boots Jill will be compared with Boots Oscar. Jill will only have an advantage over Oscar if she is superior with the same resources.
As for the exceptions: whereas Jill will equip the Full Guard when she needs the extra durability, Oscar will equip the Knight Ward (which is, if anything, less valuable during a map). I will at least mention cool things Oscar can do if he's promoted early in chapters 10 and 11, but they shouldn't hold too much influence with this argument, because I don't want to get into the quagmire of evaluating the present value of 1000 Bexp from C15 in C10. Just know that promoting Oscar early is a potentially rewarding option.
Chapter Contributions:
Chapter 1: Oscar is necessary for a 2-turn clear, where he can rescue Ike and also visit for the Seraph Robe. Jill has no contributions.
Chapter 2: Oscar's combat is valuable here. Jill has no contributions.
Chapter 5: Oscar can get Cexp himself, facilitate other units' acquisition of Cexp (thanks to his good durability), and help get some dropped treasures. Jill has no contributions.
Chapter 6: Oscar is clearly the second most valuable unit here, rescue/take/dropping Ike, damaging enemies, and contributing to the boss kill. Oscar is necessary for a 4-turn clear. Jill has no contributions.
Chapter 7: Another big chapter for Oscar. Oscar's high-mov and combat make him necessary for 4-turn (and, I believe, 5-turn) clears of this chapter. Jill has no contributions.
Chapter 8: Same as chapter 5; Oscar can help get Karuma's Red Gem. Jill has no contributions.
Chapter 9: If Marcia is not being recruited, Oscar is necessary for a 4-turn clear. He rescues and drops Ike, contributes with combat, and helps kill Kotaff. If Marcia is recruited, Oscar is necessary for the ambitious 6-turn clear (advancing Ike to the end). Oscar is similarly helpful in conventional 7-turn clears where he can advance Ike and help kill Kotaff. Jill has no contributions.
Chapter 10: A promoted Oscar is necessary for the fastest stealth clears (to rescue Mordecai). A promoted Oscar is also super-helpful in brute-force 3-turn clears. An unpromoted Oscar is still useful to recruit Kieran/Brom or Nephenee. Jill has no contributions.
Chapter 11: If Oscar is promoted, he can make major contributions to an efficient clear of this chapter (regardless whether Marcia was recruited). He can help blast through the congested middle, contribute to killing Makoya, and/or killing the Knight on the Arrive square. If Oscar, isn't promoted, he can still help get loot like the Dracoshield. Jill has no contributions.
Chapter 12: In a Marcia-rout, Oscar can help kill the two Ravens that approach the ship. In an 8-turn clear, Oscar can make many (admittedly unspectacular) combat contributions. If Marcia isn't orchestrating a 5-turn clear, Jill can make some very minor combat contributions after she's recruited.
Chapter 13: De facto rout: Oscar and Jill can both help by killing enemies. If we have not administered Bexp, Oscar's combat leads are significant and he is more valuable. If we have administered a large Bexp dump, Jill is more valuable due to her ability to fly around obstacles.
Chapter 14: Both Oscar and Jill can light the way (and clear the way) to the boss. If promoted, both can ORKO Gashilama on turn 3 (Jill needs a help with her Speed). Oscar, thanks to his ability to be smited by Mordecai, can ORKO Gashilama on turn 2.
Chapter 15: Oscar has no contributions. Jill can engage in a moderately reliable solo clear, or she can combo with Marcia for a very reliable 2-turn clear, or she can facilitate the recruitment of Stefan.
Chapter 16: Oscar and Jill can both make big (nearly identical) contributions. They have high mov, great combat, and can even ferry Mordecai. Oscar has some minor advantages here: he can be smited by untransformed Mordecai and he has an easier time getting the Speed to double Kimaarsi.
Chapter 17-1: Both Oscar an Jill can clear out the enemies in the southwest or southeast. Jill can also accomplish the more challenging feat of clearing out the northern enemies on turn 2. Boots Oscar can do the same with a bunch of shoves, but Jill can get there easier.
Chapter 17-2: Both Oscar and Jill can help transport Mordecai in the ridiculous 2-turn clear. If Marcia isn't recruited, Jill can 3-turn clear the chapter.
Chapter 17-3: Self improvement.
Chapter 17-4: Boots Jill can kill Oliver on turn 1 with a smite. Without the Boots, Jill can do the same on turn 2. Oscar is pretty worthless here if Marcia or Jill are trained. Otherwise, Oscar can lead the ground forces in a slower clear.
Chapter 18: Oscar and Jill are almost equally proficient in this chapter. They have great movement, great combat, and can ferry Reyson. Jill has a slight advantage here because she can chase down Ravens at the end over untraversable terrain.
Chapter 19: Jill can't really get the Spd to ORKO Homasa here, which is unfortunate. Jill and Oscar can contribute in a 2 or 3-turn clear of the chapter.
Chapter 20: Jill can be a major player in a 2-turn clear of this chapter (either crippling Shiharam or arriving). Oscar can (help) get Smite or Rescue (but so can Jill).
Chapter 21: Jill can contribute substantially to this clear, thanks to her ability to cut across the moat. Oscar can contribute to getting the Energy Drop or some other treasure.
Chapter 22: Jill and Oscar alike can kill the Bolting Sage in the 1-turn siege clear.
Chapter 23: Jill and Oscar can contribute substantially in this chapter with their high mov and great combat. Jill is more valuable, thanks to her ability to bypass and cover potholes, but her advantage shouldn't be overstated; it's possible to clear this chapter in 4 turns with no fliers.
Chapter 24: With the Boots and a Reyson vigor, Oscar and Jill can single-handedly execute a 3-turn clear. Jill has more flexibility thanks to her ability to fly over the river, but Oscar has the durability (with the Knight Ward) and offense to break through the bridge. Without the Boots, they can both pull off a 4-turn clear. If some other unit is arriving, both Oscar and Jill can visit the northern house for Saviour.
Chapter 25: Jill can be the best unit in this chapter, flying up to the north and cleaning house with great offense and durability. The best Oscar can do is clear out some enemies in the south.
Chapter 26: Oscar and Jill are equally capable at leading the charge to Bertram; another great performance by both units.
Chapter 27: Oscar and Jill are, again, almost identically useful. They can (help) kill Hafedd or Arrive.
Chapter 28: A 2-turn HM clear has yet to be demonstrated. If anyone can pull it off, it's Jill, but it might be just out of reach. Otherwise, Jill can assist in a straight-forward 3-turn clear over the trees. There exists, however, more involved 3-turn clears that go the long way 'round. Oscar and Jill are equally capable in such clears.
Endgame: Jill and Oscar can help clear the way for Ike and Elincia in the conventional clears. Jill's flight might be a slight advantage here (I'm not too familiar with Endgame LTCs).
Summary:Oscar and Jill are both fantastic units that can make great contributions throughout the game. Oscar has numerous unique contributions in earlygame. Oscar is necessary for the fastest clears of chapters 1, 6, 7, 9, and 10 (stealth). Jill might be necessary for he fastest clears of chapters 25 and 28 (unverified). The remainder of their contributions can be replicated by other units.
Concerning those other chapter contributions, Oscar has notable advantages in chapters 2, 10 (brute force), 11, and 14. Oscar has minor advantages in chapters 5, 8, 12, and 16. Jill has large advantages in chapters 15, 17-4, 20, and 21. Jill has minor advantages in chapters 17-1, 17-2, 18, 23, and Endgame. On chapters 13, 17-3, 19, 22, 24, 26, and 27, Oscar and Jill's contributions are very nearly identical.
All told, I believe Oscar's contributions slightly out-weigh Jill's. Recall also that my resource assumptions stacked the deck in Jill's favor. In actuality, Oscar doesn't need as many resources as Jill for the bulk of his contributions. This is another advantage for Oscar.
Oscar > Jill