Compression-based language complexity metrics show promise as holistic parameters for measuring linguistic complexity across intra- and cross-linguistic scenarios. Yet, their sensitivity to specific forms of linguistic variation requires further experimental validation. We examine the sensitivity of this metric family to register variation in Portuguese, a phenomenon already established for English. We refine the validation process found in previous literature by introducing a more granular statistical analysis to evaluate both the individual and joint sensitivity of these metrics to register variation at the sentence level. Our results confirm they are highly sensitive to functional variation in Portuguese, exhibiting the same structural morphosyntactic trade-off consistent with that observed in English and in cross-linguistic studies.