When to use internal energy and enthalpy in balances
Is it that ΔU is used for closed systems whilst ΔH is used for open systems?


That's not quite correct.

Consider the case of a simple system: a volume of gas. The problem is that when processes take place, the gas may expand or contract. Since the gas pushes back on the external pressure, some amount of work may be done the system ($W = p\Delta V$). The internal energy change $\Delta U$ does not automatically factor in this work.

Enthalpy, on the other hand, is a quantity which is defined ($U + pV$) such that it does account for the pressure-volume work of the system, so $\Delta H$ is the change the energy of the system and the pressure-volme work done by the system.

So, the summary is that if you have a constant volume process (where pressure volume work is by definition zero), use $U$. If you have a constant pressure system, use $H$.

Even the free energies are this way as well. There's Helmholtz free energy ($A$ or $F$) for constant volume processes and Gibbs free energy ($G$) for constant pressure processes.

In chemistry, most processes are done in open air (unless you're using a bomb calorimeter), in which case all processes are simply subject to atmospheric pressure, so these processes would all be best described using enthalpy and Gibbs free energy.