I'd guess there are several differences, but I will highlight one in particular. pvlib's infinite sheds model makes the simplifying assumption that light incident on the ground surface is not necessarily reflected from where it hits the ground, but rather uniformly across the entire ground surface. This means that direct irradiance incident on the ground between rows is effectively shifted to the ground underneath rows, which tends to increase the irradiance on the back side of the modules. At least this is the case currently (as of pvlib v0.12.0). Hopefully in a future version, there will be an option to simulate this reflected light more realistically.
I cannot say for sure how PVsyst does it, but my loose understanding is that it makes the more realistic assumption that ground irradiance is incident and reflected from the same point.
Kevin