In Big Five terms one study finds:
(Note... Big Five to MBTI approximations: Agreeable ~ F, Conscientious ~ J, Open ~ N)Middleborns seemed to represent the “rebellious” (laterborn) sibling in Sulloway's (1996) theory: in comparison to their siblings, they were less conscientious, less religious, and lower in school performance, as well as more impulsive and open to fantasy, whereas lastborns were the most agreeable and warm. In most cases, effects were similar in self- and mother-evaluation. Finally, mother ratings validated self-reported personality correlates of religion (Conscientiousness, Agreeableness, low impulsiveness and low excitement seeking) and spirituality (Openness).
And another study finds:
A third study finds:Across four diverse data sets, first-borns were nominated as most achieving and most conscientious. Later-borns were nominated as most rebellious, liberal, and agreeable. The same results obtained whether or not birth order was made salient (to activate stereotypes) during the personality ratings. Overall, the results support predictions from Sulloway's niche model of personality development, as well as Zajonc's confluence model of intellectual achievement.
In most studies, a significant gap between the age of sibling "resets" the birth order, so that the first child after a long gap is effectively the oldest sibling.On average, firstborns—who tend to act as surrogate parents—are more conscientious than laterborns, whereas laterborns are more agreeable, extraverted, and nonconforming.
Also note that in most of these studies, birth order effect are statistically significant, but affect the relevant trait(s)/preference(s) by less than 2%. There are some indications that birth order effects are only significant when interacting with one's family of origin. Generally, there hasn't been strong confirmation that birth order strongly affects personality.