Which has a greater dominance: hydration enthalpy or lattice energy?
The dominant factor depends on situation to situation.Here is an explanation i found helpful while predicting solubilities



The hydration energy is of Form A÷r1 + B÷r2 .



The lattice energy is of form C÷(r1+r2).
Here r1 and r2 are radius of cation and anion while A,B,C are constants.



When Size of anion is large example Iodine,Lattice energy does not decrease with increase in radius but hydration energy decreases drastically since r2>>r1(See formula)
Therefore in such cases,Solubility of Salts decreases with radius of cation.
Order- LiI is more than NaI is more than KI(in terms of solubility)



Now when anion size is comparable(eg Fluorine),The lattice energy decreases much more rapidly than hydration energy(see formula).Hence Solubility increases with increase in cationic size.Thefore order is LiF is less than NaF is less than  KF