To address the OP's question, as a complete novice yogini, what I'm really noticing is that cycling tends to flatten the lumbar curve, and a lot of yoga asana help restore neutral spine (sitting postures, the Warrior poses and various back bends are what I've done so far).

By contrast, Pilates teaches neutral spine, but in practice a lot of the exercises are done in imprint, and very few of them really do anything to increase the lumbar curve.