Energy Balances

When do you the energy balance equation which includes Delta U and when do you use the form with Delta H.

Are you referring to changes in enthalpy $\Delta H$ and internal energy $\Delta U$?

If so, you need to know the relation:

$\Delta H = \Delta U + P \Delta V$

If your system experiences a change in volume, consider the change in enthalpy. If not, you only need to consider a change in internal energy.

change in volume in what sense, a reactor would have a fixed volume. I can see the point you made from the equation you have given.