Overview & Obtaining
The button-down shirt is one of two available shirts, and superior to the T-shirt - at the slightly increased labour and material requirements. Button-down shirts can be purchased from traders, crafted, or stripped from Outlanders and Pirates.
As a complicated garment, Button-down shirts can only be made at tailoring benches, which requires complex clothing to be researched in order to be constructed. A button-down shirt requires 45 of any textile, and 125 seconds of work (7,500 ticks) to be created, assuming baseline global work speed, consciousness, sight, and manipulation.
Conclusion & Comparison
As mentioned, button-down shirts are a direct upgrade to t-shirts: they insulate better, and they protect the torso, neck, shoulders, and arms - whereas t-shirts don't protect the arms. Although this may seem rudimentary, those little bonuses can go far when combined with other pieces of apparel, and when made from the right materials - and the cost increase to make a button-down shirt compared to a t-shirt is negligible, so there's hardly any reason not to go for button-down shirts for your colonists.
The following table(s) will display how good a normal quality Button-Down Shirt is at insulating when made from various materials...