Is an iron (II) sulphate solution supposed to turn cloudy when silver nitrate is added?
According to this resource for solubility rules, $\ce{BaSO4}$ is insoluble and $\ce{Ag2SO4}$ is slightly insoluble, which would explain the the cloudiness of each solution, as well as why the $\ce{BaSO4}$ solution is cloudier than the $\ce{Ag2SO4}$ solution. 

According to this table, $\ce{BaSO4}$ has a $K_{\mathrm{sp}}$ of $1.1 \times 10^{-10}$. Comparably, $\ce{Ag2SO4}$ has a $K_\mathrm{sp}$ of $1.2 \times 10^{-5}$, which is considerably higher than $\ce{BaSO4}$. 

If you are not aware the $K_{\mathrm{sp}}$ is a mathematical measurement describing the solubility of a salt at a certain temperature (usually $25^{\mathrm{o}} \mathrm{C}$), and is found by multiplying the concentration of the salt's dissolved ions, each raised to the power of their respective stoichiometric coefficients. The higher the $K_{\mathrm{sp}}$, the more soluble a salt is. For example, the $K_{\mathrm{sp}}$ for $\ce{Ag2SO4}$ would be given by the expression: $K_{\mathrm{sp}}=[\ce{Ag+}]^2\cdot[\ce{SO4^{2-}}]$.