Judged by the following 3 the most:
Awoken Skill - Does it have better Awoken Skill (such as Skill boost, 2 Pring, Attribute Enhance)
Skill - Number of turns it takes at max skill level, or how effective is the skill.
Leader Skill - Damage magnifiers, and ease of activation
S Rank - All 3 of above are very powerful. Vegito and Awoken Ra are very popular, as many color combo damage mangifiers are strong.
A Rank - All 3 of above are very powerful, but can be difficult to use (ease of use), or difficult to obtain ideal subs. However with the ideal team, is comparable to a S Rank.
B Rank - Very Strong leader monster, but composition of team is more difficult than A Rank. Pandora and other Hero series are very strong, but since it is difficult to beat recent dungeons with things such as combo absorb and other gimmicks, they are rank B.
Leaders
S RANK
Awoken Ra
Vegito
Awoken Bastet
Juggler
A RANK
Light Kali
Awoken Parvati
Awoken Horus
Awoken Shiva
Gadeius
Ulti Goemon
Light Anubis
Awoken Lakschmi
Cloud (If Cloud System Part is Rank S)
Ulti Sarsvati*fixed
B Rank
Pandora
Wukong
Santa Sakuya
Verdandi
Urd
Skuld
Ilm
Sephiroth
Yuna
Soniagran
Subs
Subs are ranked based off 4 things. Skill, Awoken Skill, Status, and does Substitution Monster exist or not. Leader skill is not considered. I'm pretty sure Status means stats, no clue why Japanese people call it status.
Skill - Number of turns it takes at max skill level, or how effective is the skill.
Awoken Skill - Does it have better Awoken Skill (such as Skill boost, 2 Pring, Attribute Enhance)
Status - HP, Attack, RCV stats are all at least average, or otherwise has 1 Stat that is very high.
Substitution - Does it have any substitutes that you could use instead? Does it hold a unique skill that can't be replaced?
S Rank - Skill, Awoken Skill, Status are all very strong. No substitutions for that monster (is unique). Monsters with things such as 3x 2 Prongs, or stuff like Light Kali which has unique skills (not really sure what they meant by 固有スキル
.
A Rank - 2 or 3 useful color orb changing skill. When compared to S Rank, it's awoken skill or status isn't as good. However, it has very little monster you can substitute it with and is very strong.
B Rank - Stuff like 5 turn orb conversion, double conversion, in general skills that are useful in tight situations. Can be used in many parties. Awoken Skills and status falls behind A rank monsters, and substitutes exist for this monster. Is a strong sub.
S Rank
Awoken Hinogakutschi
Liu Bei
Minerva
Bakyu
Dark Kali
Light Kali
A Rank
Red Sonia
Blue Sonia
Osiris
Ulti Sun Quan
Lei Lan
Karin
Meimei
Haku
Uld
Skuld
Verdandi
Ilm
B Rank
Fire Valkyire
Water Vaklyrie
Wood Valkyire
Dark Valkrie
Yomi
Pandora
Yamato Tkaeru
Andromeda
Perseus
Wukong
Dark Izanami
Ares
Hermes
Apollon
Persephone