I'm not sure about Aspergers, you mean HFA?
This is my first time hearing of ODD, It doesn't sound very specific, almost more of a traumatic incident or diet, etc. - cause and affect. - where does ODD come from? :s
By different diagnosis you mean different doctor or different diagnostic testing?
I hope he gets a different doctor, preferably a psychometrist, and he have more than one doctor assessing him with various tools and assessments.
The pro's would be seeking more in depth advice, such as medications, diet plans, remedial interventions, anxiety training and both short-term and long-term effective coping procedures.
The con's would be money. There is probably more con's in NOT seeking a new diagnosis.
It also depends on what you hope to get out of a diagnosis, ;problems; cause and effect, ;solutions; cause and effect.
also, whatever he is diagnosed with, will you be telling him? :s it might be crucial for self understanding as well, for the diagnosis to be correct.
But I'm just a forum writer good luck!!