We present the results from a study of the morphologies of moderate luminosity X-ray selected AGN host galaxies in comparison to a carefully mass-matched control sample at 0.5 < z < 3 in the CANDELS GOODS-S field. We apply a multi-wavelength morphological decomposition analysis to these two samples and report on the differences between the morphologies as fitted from single Sersic and multiple Sersic models, and models which include an additional nuclear point-source component. Thus, we are able to compare the widely adopted single Sersic fits from previous studies to the results from a full morphological decomposition, and address the issue of how biased the inferred properties of AGN hosts are by a potential nuclear contribution from the AGN itself. We find that the AGN hosts are mixed systems which have higher bulge fractions than the control sample in our highest redshift bins at the >99.7% confidence level, according to all model fits even those which adopt a point-source component. This serves to alleviate concerns that previous, purely single Sersic, analyses of AGN hosts could have been spuriously biased towards higher bulge fractions. This dataset allows us to further probe the physical nature of these point-source components; we find no strong correlation between the point-source component and AGN activity, and that these point-source components are best modelled physically by nuclear starbursts. Our analysis of the bulge and disk fractions of these AGN hosts in comparison to a mass-matched control sample reveals a similar morphological evolutionary track for both the active and non-active populations, providing further evidence in favour of a model where AGN activity is triggered by secular processes.