This brief deals with the impact of spin-transfer torque magnetic random access memory (STT-MRAM) cell based on double-barrier magnetic tunnel junction (DMTJ) on the performance of a two-layer multilayer perceptron (MLP) neural network. The DMTJ-based cell is benchmarked against the conventional single-barrier MTJ (SMTJ) counterpart by means of a comprehensive evaluation carried out through a state-of-the-art device-to-algorithm simulation framework. The benchmark is based on the MNIST handwritten dataset, Verilog-A MTJ compact models developed by our group, and 0.8 V FinFET technology. Our results point out that the use of DMTJ-based STT-MRAM cells to implement digital embedded non-volatile memory (eNVM) synaptic core allows write/read energy and latency improvements of about 53%/61% and 66%/17%, respectively, as compared to the SMTJ-based equivalent design. This is achieved by ensuring a reduced area footprint and a learning accuracy of about 91%. Such results make the DMTJ-based STT-MRAM cell a good eNVM option for neuro-inspired computing.