Who has more natural tankiness?!

I'd say Leona vs. mixed damage, and Taric vs. AD. Taric's Shatter passive increases his and his allies' Armor, whereas Leona's Eclipse increases both her Armor and Magic resistance by a larger amount.

I prefer Leona because she has more CC.

Taric is tankier, it's very difficult to die as taric unless you 1v5 or something. Leona however has more CC and is therefore more popular.

Leona is tankier during her 'on' period than Taric, Taric is more durable during his 'off' period than Leona.

But your poll asks for 'best' and Leona is just factually better than Taric right now. Her engage pattern is more useful, she has more pick potential, she does more damage without items, and she does more during a teamfight.

She also has more of a fallback, whereas Taric is utterly useless if he falls behind, Leona can still act as a relatively effect bouncer for the adc if she's too behind to full on engage.