This is just my impression from reading about FE three houses discussion elsewhere. I won't be commenting on in-house exclusive units. (with the exception being the Church units.) Other units not mentioned here are due my ignorance in their usage.
Difficulty being Maddening for the most part.
Strong both inhouse and out of house overall.
Felix: Great growths and great major crest all help him to become a monster in combat. Can work in any physical classes. Most notable/mentioned around are Sniper, Grappler and War Master.
Lysithea: Everything said have already been said but it has been agreed that her combat can be somewhat overrated in some playthroughs. Frail magic glass cannon with the highest warp range. Notable classes being Gremory and Dark Knight. (Dark Flier gets mentioned sometimes with her because flying is that good)
Leonie: Known for being quite fast and decently tanky. Has the famed Point-Blank Volley although it does take a while to get A rank. Keep her away from mages at all cost as she can get one-shotted if not careful. Like Felix, she can be strong in any physical classes but Bow Knight is her most popular choice followed by Falcon Knight.
Petra: Another speed demon like Leonie who traded her slight bulk and PBV for better weapon proficiencies, most notably in Axes and Flying meaning that she will have an easier time reaching Wyvern Lord and Alert Stance+. (Not that Leonie can't reach those though) Other classes she is known for is Assassin but any physical class will work with her especially those that allow her to dodge well.
Contested units for strong inhouse and out of house.
Bernadetta: Her Vengeance build and the worth of her personal skill is starting to make rounds but there has been some pushback, especially those who dislike the glass cannon aspect of that particular build.
Ferdinand: His personal skill being one of the best to keep at full HP for a Hit and Dodge bonus is really effective. Pair up with Swift Strikes, and you got one godly unit. However, some have problems in regard to his recruitment difficulty. As such, he is also a contender for being strong inhouse but require a bit of investment out of house. His two classes are Paladin for pure Swift Strike and Wyvern Lord for dodgetank.
Sylvain: Ferdinand's competitor. Trades the ability for better hit and dodge for an easy recruitment at chapter 2 and the Lance of Ruin with female Byleth. Quite contested because of his poor dexterity and lacking the essential dodge that Ferdinand can provide by some. Often for many tier lists, you may find people who argue that "wherever Sylvain is, Ferdinand should be there as well." or vice-versa. Same classes as Ferdinand.
Linhardt: His utility gets brought up highly in other places especially with his combination of Physic and Warp. However reading the room here, I can see that his average magic makes his healing not as potent as someone like Mercedes plus it's not often you need two Warp users.
Strong inhouse, requires investment out of house.
Annette: The rally queen, very valuable during any Blue Lions run especially since their route grants her the magic axe Crusher. She is seldom recommended for OOH since there are other units. Notable classes are Dark Flier, Gremory, Warlock and Wyvern Lord due to her Axe access (although it's somewhat considered a meme despite how good it can be).
Ignatz: The most accurate hitter in Three Houses. Can support others with his rallies or debuff enemies with the Break Shot + Seal Strength combination. Is finding a lot more support for those doing GD inhouse runs, otherwise, he isn't as recommended out of house. His only notable class is Sniper for Hunter's Volley is required for him to accurately secure kills.
Hilda: Only available to recruit immediately in Blue Lion and locked out until way later in the game with Black Eagles Silver Snow with a very small window to recruit her. Even then, her requirement to recruit can be a bit of a hassle and her performance OOH require a bit of work for her to catch up (especially if you are going to use her in BE SS for whatever reason). Her most notable flaw is her poor dexterity not working as well for an Axe user. That being said, she is still quite an offensive powerhouse if you use her in-house.
Strong out of house, requires investment in-house. (Probably the most controversial)
Ingrid: Derided inhouse for her poor bases, and is often subjected to being benched, invested through stat boosters, or put as an adjutant until she gets better in some discussion involving BL maddening runs. OOH gives her enemy Pegasus growths which makes her far more effective when recruited at Chapter 6. Regardless of whether she is inhouse or not, she is still considered to be an effective dodge-tank especially against mages which is what allows her to stand out differently from the more offense-based Leonie and Petra, both of which have poor Res.
Mercedes: The most potent healer out of all the healers but her effectiveness is being challenged a lot elsewhere. Her biggest problem (at least with Maddening) is her delayed Physic for Chapter 2 (D rank instead of D+ like Marianne and Linhardt). While this is obviously not an end-all be all once she gets Physic, the effectiveness of Restore and most notably Fortify is also challenged due to different situations for some when put against Marianne's Silence (and her reason spell containing Thoron) or Linhardt's Warp (alongside some discussing Excalibur vs Ragnarok). However, she is considered to be a good OOH healer for both GD and BE. For GD, Marianne is sometimes considered as dancer material and Mercedes makes a good replacement healer. For BE, she can join in healing alongside Linhardt (since his magic may not be as effective depending on his growth) or be Jeritza's adjutant in CF. Another thing to note with her is that she have an alternative build as a Magic based Sniper with the Magic Bow+ (once you get the Dark Merchant).
Church of Seiros group (a.k.a Catherine, Shamir, Seteth and Cyril)
Catherine: very strong early game for BL or GD runs especially if you manage to recruit her in Chapter 4. She may or may not fall off depending on how she performs from there and what build you ultimately decide to go with her. Some rate her early game performance quite highly while some find her later game performance quite disappointing as well as her somewhat late recruitment in Silver Snow being a problem. (Although in her case, she is still useable)
Shamir: The premier Sniper available in all routes especially with how good Hunter's Volley is with only a few grinding investment. She only requires Death Blow and Hit+20 for her to be effective throughout the entire game. Although because of that, her build is quite limited to a degree and not everyone is on board with it just yet but it is growing.
Seteth: The third force that joins the Mêlée à Trois in Swift Striker users discussion. Often considered to be inferior to the other two due to the later recruitment time, and a slightly less effective personal skill. Nevertheless, he is somewhat valued due to his good base when joined and requires only a little investment to get him rolling.
Cyril: It's basically "dealing with bleh bases at Chapter 5 recruitment vs early C+ Point Blank Volley". Obviously, if Catherine is meh for Silver Snow, then Cyril is likely to be even worst especially since he scales with Commoner's growth. It's also worth noting that he can also learn Vengeance but this build is not as popular because of E rank lance but he can get there relatively quickly since lance is a boon for him. He is going to require some investment but some say that it only requires a few nudges for him to get going while others feel he is not worth it.
Ashen Wolves (minus Balthus) 😞
Yuri: Lord-like growth. Most known for being the unit with the most Speed growth at 65% meaning he will always on average, have good speed but trade for having some really cumbersome banes which limits his final class options. The bane in flying in particular fuels some debates between his performance and Petra's.
Constance: The premier black mage known for being the best Bolting user. Her dexterity can be a bit of an issue so some don't find her as reliable as Lysithea.
Hapi: Mediocre growths but have a versatile spell list. Very effective when dealing with monsters or for debuffing certain units. Have other issues such as her neutral faith means she will take time to learn Physic and Warp and her authority weakness can be an issue (although Seiro Holy Monk is already good enough.)
That is all that I know for now. Just note that these are impressions so it's not completely accurate to the more specific discussions that they have.