It does matter in my view.
With the oldest child, parents are learning how to be parents, so all the right and wrong bits are experienced with the eldest child, who tends to be independent.
The middle child gets less full-on attention than their elder sibling did, because of the division of time involved with bringing up two children. If the elder is close, the middle child can feel protected, and look to the older child as the role model. Parents tend to feel less pressure about getting everything 'right'.
The youngest child can often arrive when the parents are older and more experienced, and therefore more relaxed. there may also be more money in the household, so the youngest may experience a more relaxed regime with more luxuries, sometimes to varying degrees of resentment from the older two.
I am the youngest - i have two older sisters. My wife is the oldest, she has a younger brother and sister, and we have three girls, and my potted examples above are borne out by our mutual experiences.