Special moves for sure. By going special you avoid getting screwed by burns and intimidate,you make use of Tangrowth's best offensive stat, while also gaining some healing, that albeit weak adds up with Lefties and Regenerator. Finally if you were to use a physical Tangrowth, you would either need to use a SpD or a Spe lowering nature, and both ar very bad, since you need your speed to outspeed Scizor and you need your SpA to use Hidden Power.
Also an amazing partner for Tangrowth is Slowking. Yeah you heard well the SlowKing. Slowking covers many threats that Tangrowth can't, like Heatran, SpecsToed, Lati@s, Hydreigon, Special Dragonite, Infernape, Conkeldurr, Expert Belt/Specs Rotom-W, mixMence, Starmie, Reuniclus, Espeon and Alakazam. While he doesn't counter all of them, he checks them pretty good in combination with Tangrowth. For example if mixMence comes in against Tangrowth, you can easily send in Slokwing. Best case scenario, King takes the DM like a champ and procceeds to spread status or attack. Worst case scenario, he takes the Outrage, which he can, and then you bring in Tangrowth, getting healed in the proccess, and you shrug off the next one easily.
Also, while both seems weak against Volt-Turn teams, the truth is that Tangrowth has them covered. He outspeeds and kos Band Scizor, and is not afraid of Rotom-W, Landorus or Celebi. Finally Slowking can spread burns to make Tangrowth job easier and can phaze anything that tries to set-up on Tangrowth with Dragon Tail.