\([CuSO_4(NH_3)_2] Br_2\) and \([Cu(NH_3)_2Br_2]SO_4\) are:

Ionisation isomers

The correct answer is option 4. Ionisation isomers.

The given compounds \([CuSO_4(NH_3)_2]Br_2\) and \([Cu(NH_3)_2Br_2]SO_4\) involve the same components but arranged differently. To determine the type of isomerism, let's analyze the structures and identify the differences:

\([CuSO_4(NH_3)_2]Br_2\) - This compound consists of a copper ion coordinated with two ammine ligands (\(NH_3\)), a sulfate ligand (\(SO_4^{2-}\)), and two bromide ions (\(Br^-\)).
 
\([Cu(NH_3)_2Br_2]SO_4\) - This compound consists of a copper ion coordinated with two ammine ligands (\(NH_3\)), two bromide ions (\(Br^-\)), and a sulfate ligand (\(SO_4^{2-}\)).

Comparing the structures, we can see that the ligands and the central metal ion are the same in both compounds, but the ligands are arranged differently around the central metal ion. Specifically, the sulfate (\(SO_4^{2-}\)) and bromide (\(Br^-\)) ligands exchange positions between the two compounds.

This type of isomerism, where the connectivity of ligands to the central metal ion is different, is known as ionization isomerism. Therefore, the correct answer is ionisation isomers.