Which herb wins for roasted carrots? Thyme or rosemary?

Thyme, hands down, in my book. Rosemary seems too strong, overwhelming the gentle flavor of the carrots.

That said, if you want an easy carrot showstopper, make these - Dorie Greenspan’s Smoky Sweet Roasted Carrots: https://food52.com/recipes/78083-sweet-smoky-roasted-carrots/amp

Pro tip: You can roast the carrots and make the sauce a day or two ahead of time. Roast the carrots at high heat to heat before serving. Let the sauce come to room temperature. ;o)

The answer is yes.
Both those herbs are best with carrots.
Choose based on your own taste preference or what you are serving with the carrots.
Thyme will give more a grassy, herbal flavor. Rosemary will give a sharper flavor with piney notes.