Cotton and wool regulate heat in different ways, and most of the decision between them comes down to that difference rather than to one fibre being better than the other. Cotton is a flat, smooth fibre — it breathes well and moves heat away from the body quickly, which is exactly what you want in transitional weather, or indoors, or anywhere the temperature swings through the day.
Wool fibre is crimped, trapping small pockets of air along its length. Those pockets are what make wool warm without needing much weight — it insulates rather than simply blocking wind, which is why a wool sweater can feel warmer than a much heavier cotton one in genuine cold.
The two also age differently, which is a care question as much as a fibre one — see our care guide for the specifics on washing and storing each. In short: cotton is more forgiving of a home wash, wool asks for more care and less frequent washing.
As a simple frame: reach for cotton on an ordinary day, moving between warm indoors and mild outdoors. Reach for wool when the cold is real, or the occasion calls for something with more weight to it. Most wardrobes need both — not as a hedge, but because they're doing two different jobs.
See our care guide for washing and storage specifics on each fibre.