The large magnetoelectric (ME) coupling in the ME laminates makes them attractive for ultrasensitive room temperature magnetic sensors. Here ,we investigate the field sensitivity and signal-to-noise ratio (SNR) of ME laminates, consisting of magnetostrictive and piezoelectric layers (Metglas and piezopolymer PVDF were used as the model system), which are directly integrated with a low noise readout circuit. Both the theoretical analysis and experimental results show that increasing the number of piezoelectric layers can improve the SNR, especially at low frequencies. We also introduce a figure of merit to measure the overall influence of the piezolayer properties on the SNR and show that the newly developed piezoelectric single crystals of PMN-PT and PZN-PT have the promise to achieve a very high SNR and consequently ultra-high sensitivity room temperature magnetic sensors. The results show that the ME coefficients used in early ME composites development works may not be relevant to the SNR. The results also show that enhancing the magnetostrictive coefficient, for example, by employing the flux concentration effect, can lead to enhanced SNR.