To confirm that bones belonged to the Romanov children, which living relative would be more useful ... a relative of the tsar or a relative of tsarina? Why?

A relative of the tsarina would be more useful. The tsarina is the mother of the Romanov children and so this means she passed her mitochondrial DNA To her offspring. Mitochondria are tiny organelles in the cell that contains its own DNA outside of the nucleus. A mitochondrial DNA test is sometimes used to identify remains that are to badly degraded to perform regular DNA testing.

Since mitochondrial DNA is always passed on by the mother a maternal relative of the tsarina would be more useful.