“although" is always going to be used after the first part of the sentence. “Despite” can be used at the start of the sentnce or in the middle. “Despite having a good night’s sleep, he still felt tired”, “he felt tired, despite having a good night’s sleep”, “ he felt tired, although he had a good night sleep.” all sound natural. In my opinion if you use the word "despite" it puts a little bit of sourness into the speakers voice as opposed to “although”. Although is kind of used to tell an afterthought, despite is not.