Memristor, the two-terminal memory-resistance device discovered by Chua in 1971, is a promising solution for future processing problems. Its CMOS integration compatibility and large resistance in small size, makes it very successful candidate for large-scale systems like Neural Networks. In last decade, memristors were used in many Neuromorphic Synapses for its advantage of combining processing (dot-product) and memory in same device. There are different materials that can be used to fabricate memristors. In this paper, a comparison between spintronic and TiO2-resistive memristor in two-transistors-one memristor synapse, is introduced. The work was done on Cadence Virtuoso with using Verilog-A for memristor modeling. The comparison reveals that the synaptic implementation with a spintronic memristor is more efficient when high speed is needed. However, the resistive memristor is more adequate due to its lower power dissipation.