The $B0\to K\ast 0K―\ast 0$ and $Bs0\to K\ast 0K―\ast 0$ decays are studied using proton-proton collision data corresponding to an integrated luminosity of 3fb$\mathrm{<mrow\; data-mjx-texclass="ORD">-1</mrow>}$. An untagged and time-integrated amplitude analysis of $B^0_{(s)} \to (K^+\pi^-)(K^-\pi^+) $decaysintwo-bodyinvariantmassregionsof150MeV$/c^2$ around the $K\ast 0$ mass is performed. A stronger longitudinal polarisation fraction in the $B0\to K\ast 0K―\ast 0$ decay, $fL=0.724\pm 0.051(stat)\pm 0.016(syst)$, is observed as compared to $fL=0.240\pm 0.031(stat)\pm 0.025(syst)$ in the $Bs0\to K\ast 0K―\ast 0$ decay. The ratio of branching fractions of the two decays is measured and used to determine $B(B0\to K\ast 0K―\ast 0)=(8.0\pm 0.9(stat)\pm 0.4(syst))\times 10-7$.