Okay so I'm not exactly sure how to go about comparing relative solubilities here but I would take a gander that one could consider the intermolecular interactions that would be taking place for these types of salts.
I hate saying this sometimes but I really don't know the answer to your question at the moment.
You could look these things up in solubility tables I suppose (no Ksp's needed there) but I assume that isn't the kind of answer you're looking for.
You could try and make solutions of these things yourself and compare relative solubilities that way but again I don't think that is the answer you're looking for.
I don't see how it would be too broad. The question directly focuses on an alternative process for determining relative solubilities if Ksps were not available.
Of course you may want to state that conducting the experiment or looking these things up in tables is not really what you are looking for as an answer.
"Predicting relative solubilites of salts without Ksp values?" - In the body of your question make clear that you are aware of experimental based procedures but you are curious to know if any (semi-)reliable methods exist to predict these types of things.
Is there a way of comparing which salt is more soluble without knowing their $ K_{sp}$ data or performing experiments?
For example, comparing $\ce{Hg2Cl2}$ and $\ce{Cr2(SO4)3}$.
I am not sure but can I compare lattice and hydration energy relatively or the ion size and estimate?
Experim...
Is there a way of comparing which salt is more soluble without knowing their $ K_{sp}$ data or performing experiments?
For example, comparing $\ce{Hg2Cl2}$ and $\ce{Cr2(SO4)3}$.
I am not sure but can I compare lattice and hydration energy relatively or the ion size and estimate?
Experim...
The Periodic Table
The Periodic Table