I would say they are the same and could be used interchangeably. It is just personal preference for which one to pick.

I'd say they're nearly equal but slightly different. I don't have any grammar rule to back this up, but my interpretation would be that "I lost MY hold" means that you could get it back, but that "I lost hold of the child" is more definitive and final. For example: I lost my hold on the child and she nearly slipped away, but I grabbed her again. [The action is still resolved by you.] I lost hold of the child and she nearly slipped away, but someone else caught her. [The action has to be resolved by someone/something else.] Just my gut feeling on this one. Maybe someone else has another perspective.