Besides SYBRGreen there are other intercalating dyes such as EvaGreen used for qPCR.

Normally, you should not find relevant differences in gene expressions between both dyes. However, EvaGreen might produce slightly more defined peaks during HRM (High-Resolution Meltinc Curve Analysis), (Eischeid 2011).

For standard gene expression assays SYBRGreen has proven excellent performance and sensitivity.

Additional informationen about melting curve analysis:

Eischeid, A. C. (2011). SYTO dyes and EvaGreen outperform SYBR Green in real-time PCR. BMC Research Notes, 4, 263. https://doi.org/10.1186/1756-0500-4-263