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Transposition is the calculation of the incident irradiance on a tilted plane, from the horizontal irradiance data.
PVsyst offers two transposition models:
Hay's model, a classic and robust model which gives good results even when the knowledge of the diffuse irradiation is not perfect,
Perez model, is a more sophisticated model requiring good (well measured) horizontal data ( cf Perez, Ineichen et al.),.
Transposition is separately calculated for each irradiance component:
  The beam component involves a purely geometrical transformation (cosine effect), which doesn't involve any physical assumption. 
  The two models differ by the diffuse component treatment: 
In the Hay model, the diffuse irradiance is divided into an isotropic contribution, and a "circumsolar" part, which is proportional to the beam component. Through transposition, the isotropic part is reduced according to the solid angle "seen" by the collector plane (i.e: the fraction (1 + cosi) / 2, where i is the tilt angle). The circumsolar part is transposed geometrically as the beam component. The specificity of the Hay model is the determination of the circumsolar fraction, which is chosen as the Clearness index Ktb of the beam component.
The PerezIneichen model introduces the "horizon band" as a third diffuse component. It divides the sky into sectors, and parametrizes the transformations of the circumsolar and the horizon band according to correlations established on the basis of data of several dozen of measurement sites, distributed all over the world.
  The albedo component is evaluated in the same manner in both models, as a given fraction (the "albedo coefficient") of the global, weighted by the "orange slice" fraction defined between the horizontal and the tilted plane extension (i.e. the half sphere complement of the "seen" sky hemisphere), which is the fraction (1cosi)/2 of the halfsphere. 
The transposition models are highly dependent on the diffuse component, usually evaluated using a model (LuiJordan or Erbs correlation) which is not very well assessed.
Using measured diffuse component highly improves the transposition's accuracy.
During the early validations of the software, we tested these two models with the data of each site. The comparison of their mean errors (MBE) shows a systematic difference of 1.8 to 2.2% depending on the (Swiss) sites, while the standard deviations RMSE are comparable in all cases. It appears therefore that the Perez's model, which is more complex and especially more sensitive to a realistic determination of the diffuse irradiation, is often not justified in the PVsyst software, except for the case when measured meteo hourly data is available.
Therefore up to the version 5, by default the PVsyst software was using the Hay model.
However recent works of Pierre Ineichen [P. Ineichen, 2011] came to the conclusion that the Perez model is slightly better (in terms of RMSD) in any case, even with synthetic data. Therefore with the version 6, the Perez model is proposed as default. But the Perez model usually gives yearly averages higher than the Hay model, of the order of 0% to 2% depending on the climate and the plane orientation.
By the way you can always choose the model to be used in PVsyst (main menu: option "Preferences" > "Preferences").
You can also choose if the model that has been used will be mentioned in the simulation report.
Up to PVsyst V6.7.9 the circumsolar irradiance was always included in the diffuse irradiance for the shading and IAM calculations. This changed since V6.8.0, where a new transposition was introduced, that handles the circumsolar irradiance separately. This new transposition had to be activated explicitly by the user. Since PVsyst V7.0, the new transposition has become the default.
The switching between transposition algorithms is done either globally (for all subsequent simulations) in 'Preferences > Physical models', or at the project level in 'Project settings > Design conditions'.
The new transposition changes slightly the linear shading losses and the IAM losses. It leads to a more precise simulation, especially for large tilts, namely vertical bifacial PV installations.