Is AlCl3 more soluble in water than NaCl ?
If so why.
Should we compare the solubility on basis of covalent character, or lattice energy, or hydration energy?

No.  AlCl3  is not more soluble in water than NaCl 
More the size of the cation less will be the polarisation and its less covalent. This is according to Fajan's rule. If the compound is less covalent then its more polar. More polar compounds are more soluble in water. Here among NaCl and AlCl3, the size of Na+ is more than the size of Al3+. That means Na+ is more polar and is more soluble in water. 

Similarly when the hydration energy is more than the lattice energy the compound is more soluble in water. NaCl is having more hydration energy than lattice energy so its soluble in water quickly than AlCl3, which is having more lattice energy. 

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