Personally, I feel that my every X is a more stylised/poetic construction. Perhaps because of that, it feels slightly "dated" to me as a spoken usage.
Apart from that I think it's semantically equivalent to every X of mine. But all my X's seems a more "natural" phrasing to me, and arguably there's a slight shift in emphasis...
Every X of mine places more emphasis on all my X's, considered collectively.
My every X emphasises each one of my X's, considered individually.
Thus, for example, in...
1: John defeated every argument of mine.
2: John defeated my every argument.
...it could be argued that #1 is more appropriate where John has defeated all my arguments using a single line of attack/reasoning, whereas #2 is better where John forensically addressed and defeated each of my arguments using a different counter-argument.