Short answer--yes and no. A thick wool coat with the right construction couuld actually be warmer than a puffer with synthetic fill and sewn-through stitching.
What makes a puffer warm often isn't the fill as much as the parka-like construction with fitted wrist cuffs, snug collar, longer length, and, often, an attached hood. A good puffer will also use an outer, water-resistant, layer and off-set baffle construction to avoid cold air seeping in at the stitch lines where there is no insulation. Down fill is super warm, but many manufacturers "cheat" by using a less-than-warm feather fill with just a smidge of down. Synthetic fills aren't as warm as down, but keep their insulating properties in wet conditions where down/feathers are useless.
On the other side, a well-constructed, well-designed, quality wool coat with similar features--inner wrist cuffs, fitted inner layer to keep out wind, longer length, and snug collar might be super warm--and possibly even warmer than a puffer in damp conditions.
It also depends on your own body temperature, what you wear with the coat ( scarf, hat, gloves, boots, under layers), activity level (brisk walking vs. sitting on a cold bench, for example), and the actual weather conditions besides the temperature (wind, sleet, humidity).
From my own experience, I'd have to say my heavy, full-length, wool duffle (worn with the right outer and inner layers) was my choice on sunny cold days with temperatures hovering around -30, my fleecy, thinsulate-lined raincoat was my choice in sleety, damp winter weather, and my Canada Goose parka was what kept me toasty in winter storms when the wind was howling and exposed skin could freeze in seconds. All these coats are now way too warm for coastal winters--something that delights me no end!
