We compare two optimized chemical data assimilation systems, one based on the ensemble Kalman filter (EnKF) and the other based on four-dimensional variational (4D-Var) data assimilation, using a comprehensive stratospheric chemistry transport model (CTM). This work is an extension of the Belgian Assimilation System for Chemical ObsErvations (BASCOE), initially designed to work with a 4D-Var data assimilation. A strict comparison of both methods in the case of chemical tracer transport was done in a previous study and indicated that both methods provide essentially similar results. In the present work, we assimilate observations of ozone, HCl, HNO3, H2O and N2O from EOS Aura-MLS data into the BASCOE CTM with a full description of stratospheric chemistry. Two new issues related to the use of the full chemistry model with EnKF are taken into account. One issue is a large number of error variance parameters that need to be optimized. We estimate an observation error variance parameter as a function of pressure level for each observed species using the Desroziers method. For comparison purposes, we apply the same estimate procedure in the 4D-Var data assimilation, where both scale factors of the background and observation error covariance matrices are estimated using the Desroziers method. However, in EnKF the background error covariance is modelled using the full chemistry model and a model error term which is tuned using an adjustable parameter. We found that it is adequate to have the same value of this parameter based on the chemical tracer formulation that is applied for all observed species. This is an indication that the main source of model error in chemical transport model is due to the transport. The second issue in EnKF with comprehensive atmospheric chemistry models is the noise in the cross-covariance between species that occurs when species are weakly chemically related at the same location. These errors need to be filtered out in addition to a localization based on distance. The performance of two data assimilation methods was assessed through an 8-month long assimilation of limb sounding observations from EOS Aura MLS. This paper discusses the differences in results and their relation to stratospheric chemical processes. Generally speaking, EnKF and 4D-Var provide results of comparable quality but differ substantially in the presence of model error or observation biases. If the erroneous chemical modelling is associated with moderately fast chemical processes, but whose lifetimes are longer than the model time step, then EnKF performs better, while 4D-Var develops spurious increments in the chemically related species. If, however, the observation biases are significant, then 4D-Var is more robust and is able to reject erroneous observations while EnKF does not.