Whenever the noun precedes the possessive, it needs to be in its definite form:
gutten min (definite noun + possessive)
min gutt (possessive + indefinite noun)
"My boy" clearly refers to a specific/definite boy. Even if omitting the definite article has become the norm in English, it still carries the definite meaning.
So if I just said "det er min gutt" instead of "det er gutten min" would there be any particular difference? Because they have the same translations... Also, are both ways used or is one of them more dominant?
They're both used and correct.
However, placing the possessive before the noun can be used as a way to emphasise the ownership; making it the main focus of the sentence. Think "That's MY boy".
In cases where the ownership is not supposed to be emphasised, it's generally more common for the possessive to follow the noun than the other way around, but there are plenty of exceptions. Some of them are fixed expressions, others just sound better that way.
Until the noun has actually been introduced, we default to neuter. Once the noun has been introduced, its gender is followed.
It also can be translated as "That is my boy!" Like when your son do something good that make you proud.