Why are the bond angles in sulfur dichloride and oxygen dichloride not the same?
Why should the bond angles be the same? You have different atoms every time leading to different molecules. Different molecules have different properties; that goes both for macroscopic properties (they will have different melting and boiling points, their liquid phases will have different densities and refraction indices) and microscopic ones (i.e. their molecular structure will be different). Indeed, there are three-atom molecules with a $90^\circ$ bond angle and those with $180^\circ$. I’m not sure whether it ever gets any smaller than $90^\circ$ but I suspect ‘no.’