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Using an atomistic full-band quantum transport solver, we investigate the performances of vertical band-to-band tunneling FETs (TFETs) whose operation is based on the enhancement of the gate-induced drain leakage mechanism of MOSFETs, and we compare them to lateral p-i-n devices. Although the vertical TFETs offer larger tunneling areas and therefore larger on currents than their lateral counterparts, they suffer from lateral source-to-drain tunneling leakage away from the gate contact. We propose a design improvement to reduce the off current of the vertical TFETs, maintain large on currents, and provide steep subthreshold slopes.