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So I will start by saying I main Anivia and am biased.
I think her kit shines on TT2 because there are so many nice chokepoints on the map now. On TT I play her as a kind of bruiser mage. Since most games it's Olaf, Panth and Lee Sin or something along those lines Frozen Heart and AA Staff work great on her and the MS from Wooglet's Witchcap works out very nicely with her kiting ability.
Overall I think with a tanky build and the right playstyle she can be a very high threat on the new TT.