考究 it something like inspect and research, we don't use it in speaking even writing, so you can't find it in books of the word. 讲究 it is Vber and adjective, something like "pay attention to" 我不是一个特别讲究整洁的人,I am not a particularly orderly person.

Usually， 考究 = 讲究 1. v. to emphasis, to focus on, 2. adj. exquisite, subtle !!!!!! 1) 讲究 is with a unique meaning : deliberate, weighed with patience. eg. 这件屋子的布置大有讲究。（here it means "the settlement of the room is quite good which shows a perfect assemble."） 2)考究 is with one more meaning that is "研究，考察"（to do researches）. And 考究 is used in writing more often because it just wears a sense of formality （I mean, it's quite formal）