What do you mean by "hydration energy"?
Acidic strength is proportional to the amount of hydronium ion formed by a given amount of the acid. It is also defined as the activity (rather than the amount) of the hydrogen ion. All acids that form in an aqueous system can only produce an acid of the same strength as hydronium ion. In non-aqueous systems, the nature of the anion and the nature of the stabilization of the proton in solution determine the strength of the acid. Search "Olah, acids, superacids" for more detail.
The stability of the anion formed by the acid is usually determined by the acidity itself! The more acidic... the more stable. The more completely dissociated... the more stable.