Hey guys,
Taric main for about 6 months now (probably 350 games total with him across all my accounts). Taric's carried me from Gold 5 to Plat 3-ish now, so I'm definitely a fan. So first of all, I'm also a big fan of Leona and Braum, but Taric offers something different than both of them, and that's the ability to keep your entire team alive through a chaotic fight.
Let me discuss build philosophy first and then I can explain how Taric can do what he does.
First of all, Taric synergies best with the following stats:
Armor
Health
CDR
My General Build path goes as follows:


Generally speaking in that order, but building components as I go along. Sometimes Aegis gets prioritized if the team is AP heavy. note I do typically get
earlier in the build but I sell them by my 6th item.
This build does a few things:
40% CDR and upwards of 400 Armor
This means, in a teamfight I get off an average of 3 heals, 2-3 stuns, a Face of the Mountain Shield, an Iron Solari Shield, and also giving my teammates about 45 flat armor. Zed very literally cannot kill my carry. No Exhaust necessary.
Runes:
Flat Attack Damage Marks
Flat Magic Resists Glyphs (or Scaling if vs non AP Support)
Flat Armor Seals
Flat Armor Quints
Masteries:
0-17-13
Laning Phase:
Starting Purchase:
Typical laning phase is weak until your first back so I play passively while leveling skills in the following order:
First 3 levels: E-Q-W
Then prioriritize R-E-W-Q
This will give you the best engage possibility. Taric is fantastic at setting up Jungle ganks with the increase stun duration from leveling e.
Mid-Game
Typically, you have sightstone, some components of face of the mountain and glacial shroud. This gives you reasonable health and armor with at least 20% cdr. In fights, always fit in auto-attacks in between your spells for extra damage.
Late-Game
You're a walking behemoth. You do plenty of damage because of the armor shred on W (which also deals more damage as you get more Armor) and you're rotation of spells is quite literally one after another ala Ryze. Taric can 1v1 straight up many AD champions (Riven, Zed, Master Yi). Your job in teamfights is to heal/shield the highest priorities targetted teammember and keep them alive, and you have tons of tools at your disposal to do that.
Weaknesses:
Janna is probably one of Taric's biggest counters. Taric's stun is too slow and Janna can shield most of his harrass and engagement potential. AP based teams (AP Mid + AP Top) also provide some trouble for Taric since it doesnt allow him to build as much armor (build a spirit visage instead of Thornmail and probably build it earlier). Other AP supports offer some annoyance but you can weather the storm until mid game typically by playing a conservatively and healing your ADC.
Bottom line: So Taric vs Leona:
Leona starts out tankier than you, she will probably deal more damage initially, but you outscale her pretty well with utility over time. The targetted stun, although a slow moving projectile means its not dodgeable, and therefore is great for junglers to follow up. Early levels, you sustain past your enemies with your heal but by mid game, you're a beast. Able to initiate pretty reliably on a single target and just being to tank a lot of damage and able to live through it.