People are using Aether to decide this. Allow me to use actual game knowledge to decide this. Note, Awakening units are stronger than Fates units, due to different base states, and growths.
Chrom: Chrom has the Lord class, and starts out using only swords. Upon promotion, he gains the access to lances. He, Lucina, and Marth are the only ones capableof using a Falchion, as well as the rapier. Falchion grants extra damage to dragons and wyvern riders, while the rapier grants extra damage to beast units, cavalry, and armored foes. He has good HP, Strength, Speed, Luck, Defense, and Skill growths, but terrible Magic and Resistance growths. The Skills he learns from the Lord class line are Dual Strike+, Charm, Aether, and Rightful King.
Ryoma: Ryoma has the Swordmaster class, and is sword locked unless he reclasses, either due to a Heart Seal, Partner Seal, Friendship Seal, or a special DLC Seal. He is the only character capable of using Raijinto, a sword that attacks from either Range 1 or Range 2, and while lowering Defense and Resistance by 1, boosts Speed by 1 and Strength by 4 when equipped. He has good HP, Strength, Speed, Skill, and Luck growths, middling Defense and Resistance growths, and terrible Magic growths. The Skills he learns from the Samurai-Swordmaster class line are Vantage, Duelist's Blow, Astra, and Swordfaire, with his own personal Skill, Bushido. As a Master of Arms, he learns Seal Strength and Life and Death. We however, won't count those, because it would require a reclass. We aren't reclassing Chrom, so no reclassing Ryoma.
Comparison: Due to the differences between Awakening and Fates, we will need to make this as fair as possible. Whether that has giving Ryoma Awakening bases and growths, or giving Chrom Fates bases and growths, I'll leave that to you. In either case, Chrom will have more HP, Defense, and Luck, while Ryoma will have more Speed, Skill, and Resistance, with equal Strength growth. In terms of weapons, Raijinto is more useful than the Falchion. Sure it slightly lowers the defensive stats, but it increases offensive stats, and can be used from Range 2. Sure, Falchion does more damage to dragons and wyvern riders, but Ryoma doesn't have dragon weakness, so no point. Dual Strike+ and Charm are supportive skills, so they're useless. Aether is Sol and Luna in succession, and Chrom is capable of activating a critical for each strike. With the Sol portion, Chrom heals half the damage he dealt, and with Luna, he ignores half the opponent's defense. Rightful King increases chances of Skills activating by 10%. For Ryoma, Vantage has him attack first if he's below 50% health, regardless of who atacks first. Duelist's Blow increases his dodging rate by 30, should he initiate battle. Astra has him attack five times in a row at half damage for each strike, but he can critical for every single hit. Swordfaire has him do +5 damage when using a sword. His personal, Bushido, has him deal +2 damage and take -2 damage, should his opponent be of equal level, or higher level than Ryoma. Chrom can use more weapons as a Great Lord, but the fight would likely be between Falchion and Raijinto, so we're keeping it between them.
Results: This one is close, all things considered, but the edge goes to Ryoma. With higher Skill, he's likely to activate Astra, and critical more than Chrom, his higher Speed could possibly have him double Chrom, and help him dodge Chrom's attacks, as well as Ryoma having naturally high dodge rate anyway. Chrom has an edge defensively, with higher HP, Defense, and Luck, but Ryoma's higher offensive stats, with the boost added by Raijinto, and Raijinto's Range 2 capabilities, makes it hard for Chrom to deal. Aether and Rightful King certainly keep him in battle, but Ryoma has more useful Skills for the fight than Chrom does, so more at his disposal. And if we're counting lore, Chrom is noted for having a poor tactical mind, while Ryoma is noted for winning every battle he has competed in, due to his astute skill as a tactician, and being considered the best swordsman in all of Hoshido. Chrom will hold his own in the fight, but Ryoma will claim the victory in the end.
