To answer the question above: no, an organic textile is not necessarily more responsible than a non-certified textile . To understand this inconsistency, we need to look at how the fabric is made. For an organic fabric, for example, only the cotton fields are treated without pesticides. The transport of the cotton, workers' wages, or even the dyeing process are not taken into account in the certification. As for a GOTS-certified fabric, the entire production, manufacturing, and marketing process is controlled.
To better understand these differences, here is an explanatory table of the similarities and differences of each textile certification: