Here's a breakdown of the Pro's/Con's of each path:
Overtuned Origin grants 1 bonus pick and reduces AP cost on Biomorphosis by 1.
Clone Army Origin must take Cloning
Evolutionary Predators Origin must take Mutation
Wilderness Origin must take Purity
Cloning:
Clone Vat Assembly doubled(1.5 -> 3), limit of Clone Vats increased to 4 via Cloning finisher(cap based on Tier of Capital Building). Requires 3 extra Build slots for those Clone Vats though.
Maximum of 8 Trait Points/7 Picks
Cannot add Negative Traits
Cannot remove Overtuned Traits
Cannot remove Positive Traits*
*Can remove Growth Traits via Somatic Synthesization Tradition. These include Rapid Breeders, Incubators, Existential Iteroparity, Egg Laying(Growth Phenotype Trait, hence special case), Fertile, Exotic Metabolism and Vat Grown(which can be freely added removed since cost is 0). Can also remove Vocational Traits via Targeted Gene Expressions Tech. These include Agrarian, Industrious, Ingenious, Intelligent, Charismatic, Thrifty and Traditional. Can also remove Pre-Spaient Traits with Epigenetic Triggers Tech.
Mutation:
Auto-modding is the easiest
Adaptive Mutation Trait yields Pops that are the most efficient for the job and result in 15% Efficiency boost, including Alloys/CG. This stacks with other Traits like Erudite or Natural Machinist
Maximum of 8 Trait Points/9 Picks
Can remove virtually any Trait you want save for Overtuned Traits(may be wrong here but I'm pretty sure I'm correct)
Can add virtually any Trait you want, including Phenotype Traits of any species
Purity:
Maximum of 10 Trait Points/7 Picks
Can remove any Organic Trait in the game, including Overtuned
Can add virtually any Trait in the game save for Phenotype(must match species subset).
Advanced Trait cost(excluding Exotic Metabolism) reduced by 1.
Creates a Genetic Purity Score. Score is based on sum total of Positive Traits(before their cost is reduced) + Overtuned Traits and subtracts sum total of Negative Traits. Any traits obtained via Orbital Speed Demon event count towards this at 1 point each. Purity Score is used for Advanced Government Authorities.
Each Flexible Tradition choice results in Empire Modifiers being applied. Up to two bonuses are granted from each path. Each path yields the following:
Cloning: +1 Assembly per 100 Genomic Researchers. +300 Amenities per 100 Genomic Researchers
Mutation: +10% Habitability from Genomic Research Lab. +100 Pops Auto-modded per month.
Purity: +10% Pop Growth per 100 Genomic Researchers. -1 Maximum Negative Leader Traits
As for Flexible Traditions...
Tier 1: Best one is Environmental Integration or Mutation. Mutagenic Habitability is just too good to pass on in my opinion. Having the Habitability cap raised from 100% to 200% can result in +25% Job Efficiency, -25% Housing usage and -25% Amenity usage. If you take Adaptability Tradition and optimize your Planets(ex: Gaia/Ecumenopolis), then your floor will be 160%(140% on Relic Worlds). It does not mean that the other two options are bad. Purity's choice is a great option if you're looking to maximize your Leaders while if you're aiming for insane Pop Growth, then Cloning's Genomic Growth cannot be beat.
Tier 2: Purity's Heightened Abilities is best option here and honestly the default pick due to -10% Empire Size from Pops. If the other options granted Empire Size reductions too, then we might have some competition.
Tier 3: Choice really comes down to Cloning(Biochemical Composure) or Mutation(Nucleotide Isolation). Purity's choice is so bad that I don't like to even mention it. The only reason I would even take Purity here is if you really wanted the Empire Modifier(-1 Negative Leader Trait) or you wanted to take Purity Tradition path and hadn't taken a Purity Flexible Tradition. Anyways, of the two reasonable options, either one works. Cloning grants Backup Clone Trait to all existing and future Leaders. The Trait is a cheat death trait(which means it'll reincarnate them) but while they have it, they get +2 Effective Leader Skill. This means better Dig Site skill, Astral Rift skill and better Councilor perks(including Agenda Speed). Yet if they die, they gain a malus trait that can only really be mitigated via Purity's option on Tier 1 and Cloning Authorities(Democratic being the best).
As for Mutation, this is the **ONLY** way to gain Nucleotide and Leviathan Traits. Nucleotide Traits are obtained from the Orbital Speed Demon event and have been significantly buffed. Leviathan Traits can only be added if you've killed the prerequisite Leviathan. If you don't have any Leviathan's to kill, then this Tradition is kind of weak.
Recommended Flexible Path: Mutation -> Purity -> Cloning