New developments in pressure- and thermally driven membrane desalination technologies offer the potential to cost-effectively treat high-salinity waters, especially when powered by low-cost solar electricity and thermal energy. This paper presents a comparative techno-economic assessment of the state-of-the-art most promising pressure- and thermally driven membrane technologies for high recovery desalination, namely, osmotically-assisted reverse osmosis (OARO) and batch-operated vacuum-air-gap membrane distillation (batch V-AGMD), to produce potable water while concentrating brine within the range of 140–290 g/L TDS for minimum-liquid-discharge (MLD) and zero-liquid-discharge (ZLD) applications. It is shown that both OARO and batch V-AGMD can treat feedwater and brines with TDS in the range of 30–125 g/L with corresponding fresh water recovery rates of 85–25%. When low cost solar electricity and thermal energy are used, the resulting levelized cost of water (LCOW) from OARO is in the range of 0.70–6.28 $/m3, and that from batch-V-AGMD is in the range of 1.74–2.77 $/m3. OARO is more cost-effective than batch V-AGMD when feedwater salinity is below 70 g/L and recovery below 75%, whereas batch V-AGMD is more cost-effective at higher recovery rates and salinity levels. The sensitivity of this comparison on energy prices and module costs is discussed.