MicroRNAs (miRNAs) have been shown to modulate gene expression noise, but less is known about how miRNAs with different properties may regulate noise differently. Here, we investigate the role of competing RNAs and the composition of miRNA response elements (MREs) in modulating noise. We find that weak competing RNAs could introduce lower noise than strong competing RNAs. In comparison with a single MRE, both repetitive and composite MREs can reduce the noise at low expression, but repetitive MREs can elevate the noise remarkably at high expression. We further observed the behavior of a synthetic cell-type classifier with miRNAs as inputs and find that miRNAs and MREs that could introduce higher noise tend to enhance cell state transition. These results provide a systematic and quantitative understanding of the function of miRNAs in controlling gene expression noise and the utilization of miRNAs to modulate the behavior of synthetic gene circuits.