Fates - Common Unit Breakdown

Kamui/Corrin
Nohr: S
Hoshido: S
IK: S
Great growths that allow you to put priority on what you need, amazing Prf sword, tanky when it really matters (early game), choice of any class you want, Dragon Fang, Draconic Curse. Personal really helps early game, as well.
Major issue is that you can get two-shot by a lot of things later on, especially since the upgraded Dragonstone is hot garbage.

Aqua/Azura
Nohr: S
Hoshido: A
IK: S
Refresher units have always been very good, and she's no exception. She also comes with crazy good offensive growths, for some strange reason. She gets a skill early on that makes her refresh even better. With Rescue and a bit of work, you can even have her refresh multiple times a turn, but that's only for when your absolute best unit really needs that boost. In Hoshido she's a little worse because the best strategy there is generally to just run into the fray, but she can still buff the guy that does that stuff.

Felicia
Nohr: A (male avatar), C (female avatar)
Hoshido: A (male avatar), C (female avatar)
IK: A (male avatar), C (female avatar)
Very helpful early on, debuffs are useful, heals better than your little sister does at the start. Her personal gives Kamui a great boost early on. She's a prime candidate for an early Parallel Seal to Strategist, which will take advantage of her higher magic stat and give her the ever-useful Battle Command. Her growths are kind of lacking, but she can be replaced by a captured Maid/Strategist if it's truly necessary.
It's worth noting that, even though she's a promoted unit, she gains EXP just like an unpromoted unit would. Her natural level cap is 40, as well.

Joker/Jakob
Nohr: S (female avatar), C (male avatar)
Hoshido: S (female avatar), C (male avatar)
IK: S (female avatar), C (male avatar)
Like Felicia, but with more of a physical focus. He won't heal for quite as much, but his personal skill is unmatched. Also similar to Felicia, he loves an early Parallel Seal, but this time to Great Knight. If you're playing with a female avatar, there's really no good reason not to marry him, gameplay-wise. Especially if you use a dodge-based class (Trueblade, Elite Ninja, even Witch) or General. If you use Joker/Jakob, he stays right in your pocket until the very end.
It's worth noting that, even though he's a promoted unit, he gains EXP just like an unpromoted unit would. His natural level cap is 40, as well.

Silas
Nohr: B+
Hoshido: A
IK: A
Has a relatively rare starting class with some pretty great growths, and a neat personal skill. It's kind of hard to keep it active, but when it is it helps him take a ton of punishment. Rescue's a great skill as well, and he has a really strong daughter. He even has Merc secondary for the coveted Ghetto Aether combo, or just to have a balanced and strong Hero that's faster than Harold/Arthur. I'd say he's not AS great in Nohr just because Marx/Xander really steals his thunder, but he's still very worth using. In IK, he's one of very few late-joining units that DOESN'T get shitty base stats. In fact, they're amazing.

Suzukaze/Kaze
Nohr: C+
Hoshido: C
IK: C
He's a ninja, and that's great. His personal is pretty much "I give my partner Miracle," and that's neat. But he has some of the most depressing growths ever. Between his brief appearance in the common route and his recruitment in Nohr 11, he gains a whopping TWO Strength in six levels. As a physical unit, having a coinflip Strength growth is really lame, and it often gets to the point where all he can do is debuff and dodge some things. I give him a C+ in Nohr just because he's the only base-class Ninja in the route, yet I don't feel comfortable giving him a B.

Mozume/Mozu
Nohr: B+
Hoshido: C
IK: C
Mozume/Mozu is the Donny of this game. Complete shitter bases, difficult to bring up, but Aptitude makes her a killing machine given enough effort. Like Donny, she prefers being reclassed instead of staying in her base class. But Aptitude has been slightly nerfed, from +15% growths to +10% growths.
In Nohr, if you recruit her immediately when she's available, you have her recruitment chapter, chapter 8 (once you've dealt with the three-village objective), and chapter 9 to take things slow and baby her. She's the only one who can become a full-fledged Bowman without taking marriage into account. However, Parallel Seals are in short supply early, so it makes the choice difficult. Later on, she becomes a hardcore ninja-killer and a "fuck this guy especially" kill-button.
In Hoshido and IK, you have a couple other Bowman, so it's a little harder to justify her use. Things are pretty rough at the start in IK, but in both cases, grinding is available should you choose to do so.
People who like to play fast/efficient should just ignore her, naturally.

Ashura
Nohr: A
Hoshido: C
IK: B+
He's an acceptable healer and great Thief, coming into Nohr where Zero's kind of starting to show off his shitty Strength growth. In Hoshido, he comes in very late with some pretty lame stats. But in IK, he comes with the same exact stats seven chapters earlier (according to the Wikia at least). If you so choose, he can be your ace-in-the-hole for cheesing Nohr's final chapter. Or you can just kill him for his shoes, if you want to be brutally efficient.

Izana
Nohr: C
Hoshido: C
Eh. You're forced to spend DV points on the bathhouse for him, and he comes with some pretty lame speed for his class. He can be an okay staffbot if you want, but then so can anyone else. Honestly, I often forget he's even recruitable.