I say kalista because of her mobility and sustain but draven has click and throw.
Kalista's mobility is reliant on her getting within 550 range of a target. Draaaaaaven has 550 AA range.
Kalista's passive doesn't mean diddly against Draven. It will make his axes mildly more annoying to catch, and that's it.
Also - Kalista's ultimate doesn't do dilly squat in a 1v1.
All Kalista has going for her is less than 32 damage per-hit from Rend spears.
Draven has 85% of his AD on each AA with Axes. With base stats alone (~110 AD at 18), that's a lot more than less than 32 damage per-hit via Rend.
Kalista being strong in a 1v1 is mostly just against low-mobility bruisers. Anyone that can reliably hit her back can reliably beat her in a 1v1.