We present the analysis of a sample of twenty-four SLACS-like galaxy-galaxy strong gravitational lens systems with a background source and deflectors from the Illustris-1 simulation. We study the degeneracy between the complex mass distribution of the lenses, substructures, the surface brightness distribution of the sources, and the time delays. Using a novel inference framework based on Approximate Bayesian Computation, we find that for all the considered lens systems, an elliptical and cored power-law mass density distribution provides a good fit to the data. However, the presence of cores in the simulated lenses affects most reconstructions in the form of a Source Position Transformation. The latter leads to a systematic underestimation of the source sizes by 50 per cent on average, and a fractional error in H0 of around 25-19+37 per cent. The analysis of a control sample of twenty-four lens systems, for which we have perfect knowledge about the shape of the lensing potential,leads to a fractional error on H0 of 12-3+6 per cent. We find no degeneracy between complexity in the lensing potential and the inferred amount of substructures. We recover an average total projected mass fraction in substructures of 103 fsub < 1.7-2.0 at the 68 per cent confidence level in agreement with zero and the fact that all substructures had been removed from the simulation. Our work highlights the need for higher-resolution simulations to quantify the lensing effect of more realistic galactic potentials better, and that additional observational constraint may be required to break existing degeneracies.