Both come off an animal that lives somewhere cold and high, both are finer than sheep's wool, and both cost more than you'd like. After that they part ways. If you're choosing between them, here's what the difference actually feels like in use, rather than on a spec sheet.
Softness
Cashmere wins, and it isn't close. The down from a cashmere goat runs around 14 to 16 microns, which is fine enough that it sits against the neck without a hint of scratch. Yak down is a touch coarser, roughly 16 to 19 microns depending on the animal and the part of the coat. That's still soft, softer than any sheep's wool you've worn, but next to good cashmere you can feel the extra bit of substance. Whether that matters depends on you. Some people want a cloud. Some want something with a bit of backbone.
Warmth
Yak edges it. Yaks graze above 4,000 metres, and their down is built for that, with good insulation for its weight and a natural resistance to damp that cashmere doesn't share. Gram for gram the warmth is close, but yak tends to feel warmer in wind and won't go limp if it gets a little wet. For a piece you'll actually wear outside in winter, that counts. Our handwoven yak shawl is the warmest cloth we make, and that's the reason.
Durability
Yak again. The slightly thicker fibre and a tighter natural crimp mean it resists pilling better and holds up to being worn hard. Cashmere is the more delicate of the two, and it pills where it rubs and wants gentler handling. Neither is fragile, but if you're rough with your things, yak will forgive you more.
Weight and drape
Cashmere is lighter and drapes more fluidly, which is why it suits a scarf or a piece you fold away in a bag. Yak has more body, so it holds a fold and sits well as a proper shawl or wrap. This is less about quality than about what you want the thing to do.
Price
Cashmere is dearer, mostly because the supply chain is older and the demand is enormous. Yak is still relatively niche, which keeps it more reasonable for a comparable amount of fibre. You're often getting more warmth per pound with yak, if not more softness. If you want the full picture on the other fibres we use, our guide to the different wools lays them out side by side.
So which
Cashmere if you want the softest thing against your skin and you'll treat it kindly: an evening wrap, a fine scarf, something light. Yak if you want warmth that earns its keep outdoors and survives daily wear. Plenty of people end up owning both for different jobs, which is the honest answer nobody selling one of them likes to give.
We've put wool and cashmere head to head too, and the longer view on how we weave any of them is in the Guide to SHAAL.