An anaerobic membrane bioreactor and aerobic granulation technologies were tested at laboratory scale to treat winery wastewater, which is characterised by a high and variable biodegradable organic load. Both technologies have already been tested for alcohol fermentation wastewaters, but there is a lack of data relating to their application to winery wastewater treatment. The anaerobic membrane bioreactor, with an external microfiltration module, was started up for 230 days, achieving a biogas production of up to 0.35 L CH4L−1d−1 when 1.5 kg COD m−3d−1 was applied. Average flux was 10.5 L m−2 h−1 (LMH), obtaining a treated effluent free of suspended solids and a chemical oxygen demand (COD) concentration lower than 100 mg COD L−1. In contrast, the aerobic granular sequencing batch reactor coped with 15 kg COD m−3d−1, but effluent quality was slightly worse. Aerobic granulation was identified as a suitable technique to treat this kind of wastewater due to excellent settleability, high biomass retention and a good ability to handle high organic loads and seasonal fluctuations. However, energy generation from anaerobic digestion plays an important role, favouring anaerobic membrane bioreactor application, although it was observed to be sensitive to sudden load fluctuations, which led to a thorough pH control and alkali addition.