If you are talking about end game stuff not sure what you are really talking about... O.o ChenA is broken, RumiaP effectively has base 217 spread attack and DaiyouseiD makes for an extremely potent late game wall. Also Wakasagi Kogasa, the list goes on and if you include 90 cost as well then you have KeineD and MomijiS which are both powerhouses.
Higher cost might have a slightly higher total base stats but not enough to make a significant difference in your choices for late game puppets and a level 100 80Cost will have far more stats than a level 81 120 cost. The more important factor is where the stats are allocated typing movepool and ability.
Unless you are talking about building competitive teams and then unfortunately you are optimizing for the best possible thing you can do (though 80 costs still have a chance there) but trained 80 cost puppets can easily dispatch all the post game fights.
Kasen's wilds are the best EXP until you can solo Yuki rematch (a level 100 Chen should have no troubles) then just keep killing her and reseting.. Aya is probably the best puppet for grinding others as she can quite easily solo Yuki, Mai and Yumeko before gapping back to start again. You should be able to get 2 6S rank puppets in about 50-100 magical fragments and then from there it will only take like 10-20 fragments to make perfect puppets. Fastest place to farm fragments is Mayohiga but you should get tons from exp grinding in general as literally everything in the game has at least a 20% chance to drop fragments if they drop an item.
Might make a video on how to make 2 6s rank puppets efficiently at some point but... lazy x.x
Power Rumia is completely USELESS, because she cannot stand damage AND is too slow.
Defense Luize is completely helpless aswell, because she's just not fast enough to make the opponent flinch, while flinching is the main reason to have her secondary effect boost. That is, if she's lucky enough to make the 60% flinching actually work.
Defense Keine (I'm assuming with Hakutaku ability) is barely any useful aswell, because it takes her to take damage AND remain alive to start kicking some ass. That is, if she's quicker than her opponent after transforming.
Assist Akyuu is a joke aswell, because if on the paper she might be able to kick some ass by trapping the opponent in a slow and agonizing death, the reality is that just every enemy puppet is polyvalent enough to have at least one move to beat up the poor Akyuu.
Assist Kotohime is the worst, with her very average stats, her lack of powerful moves, lack of defense, and a next to useless ability.
And besides this, all the Cost 110-120 that I have raised have their fair share of fearsome power and/or speed. My only useful 80 power that I tried are Speed Dai, Power Lily (both for Fairy Dance+Energy Absorb), and Assist Chen. All the rest is MEH.
Sure you do can make something not too bad out of some 80-90 cost, but that just won't cut out the fact that 110-120 remain superior to them. Even if these 80 Cost are playable, it takes them quite some strategy to make something out of them, while Cost 110-120 can just spam the bigass powerful attacks and call it a day. And the "bigass attack spam" is basically all the endgame is made of, by the way.