Both of these two words 条 and 根 in the dictionary are said to be measure words for long and thin objects. What are the differences between them?
條 can be a measure word for huge things. For example, 一条河, 一条烟囱, 一条船(all long and thin but huge) - you can't use 根 for huge things
条 can be a measure word for living things. For example, 一条蚯蚓, 一条蛇, 一条狗 (all long and thin and alive) - Don't use 根 for living things
条 can be a measure word for thin and long things with flat surface, For example, 一条手帕. 一条毛巾 (both long and thin and have a flat surface) - You can't use 根 for things that have a flat surface
条 can be a measure word for abstract concepts. For example, 一条规矩, 一条题目
根 is more common when used as a measure word for tiny things. For example, 一根绣花针, 一根火柴, 一根松针, 一根头发, 一根汗毛, (all long, thin and tiny)
条 can also replace 根 when used as a measure word for tiny things especially objects from living things. For example, 一根头发, 一根汗毛; 一条头发, 一条汗毛
For things that are not huge, tiny, alive or have a flat surface 條 and 根 are often interchangeable. For example, 一条长棍, 一根长棍, 一条短棒, 一根短棒
Starting from the essential meanings of these two measure words, 条 is the small branch of tree, and 根 is the root of tree. In daily conversation, 条 is used for things that may be long and wiggly, such as 一条河(river), while 根 is for long, straight objects, such as 一根香菸(cigarette).
Sometimes, 条 and 根 are interchangeable, we can say 一条 or 一根 香蕉(banana), or 香腸(sausage).
My experince is that 根 is used for small and hard objects such as 铅笔，香蕉，香烟， etc. Well, 条 is usually for big and soft ones like 蛇，河，船， 围巾，etc.