The same. But we often use "几岁" when she/he is less then 10 years old.

他多大？ or 他几岁？ -> 他(今年)多大了？ or 他(今年)几岁了？ Generally speaking, they are same. If we have to find the diffreences between them, we can try to distinguish them from the point of occasions. I think, " 他(今年)几岁了？" are mostly used when we ask a younger generation, e.g., You ask the age of a child of your friend. While " 他(今年)多大了？" can be used to ask the age of any "他" and maybe often used in Oral Chinese. Moreover, ask the age of a person, we often add " 今年 " to avoid some misunderstanding.

他几岁only can be used on children or people who is much younger than you,他多大 often used between the people in the same age range, to show your respect.

他多大？一般是对小孩子或者和自己同辈的人说的。比如说，隔壁的小王多大了？ 但是他多少岁，会比较正式一点，对于比自己年长的或者辈分高于自己的一般会说，比如，隔壁的王爷爷，他今年多少岁了呀？

Means the same But 他多大？ More commonly used