The RO membrane is the work horse of an RO/DI water purifier. It removes >90% of the TDS from your input water, and the DI 'polishes' the water coming out of the RO membrane.
If you're going to only use one, go for an RO membrane. DI resin probably the most expensive part of an RO/DI system, and you'd be burning through it very quickly if you were using DI alone to clean up your tap water.