The Pseudo-Voigt and Pearson VII line fitting methods use a mixture of Gaussian and Lorentzian profiles, however, they are not very good models when peak asymmetry is present (as happens a lot in XRD).

The split functions can handle peak asymmetry much better as the low and high sides of the peak are modelled independently. These are perfectly fine for single line fitting, but with a full profile there are very many parameters to refine (6 per line). A disadvantage of these is that microstructural information cannot be  extracted from them.

The preferred option for full pattern fitting is to use Fundamental Parameters, a convolution based approach that can deal with microstructure. You will need to have all the geometrical information of your diffractometer included. You can save these settings and have TOPAS start up with your instrumental profile each time. It is good to start out to use a standard material and refine the parameters such as Tube Tails. As your tube ages it may be necessary to repeat this. Having said all that, I still choose SPV if I want to model an amorphous peak, but for all my quantitative work I use FP exclusively.

I totally agree with Ian. What he did not mentioned: play a little bit around by yourself. It is important to get an impression, how far you can come with each model, and how much the results finally differ. Often, for quantitative phase analysis the difference for each model are not that dramatic although the difference plot looks "horrible". Only if you really need to go to the limits without a good approach of the profile the results are often not totally wrong but also not the best. Ian already mentioned that he is using FP if it is very important. The reason: all the mathematicla functions are approximations developed over the years. They are based on experiences only and do not have a real physical meaning, although correlations have shown that specific parts are representing strain (no ideal translation symmetry) of crystal size. Start with fix data like  constant FWHM and then step by step increase the number of free parameters. If you don't do this, commonly the same diffractogram can be described by different compositions but changing parameters. It is a software, which only in rare cases automatically delivers a reliable solution. However, if you roughly understand which are the traps and how reliable parameters look like, it becomes very common in use.

As Ian, I also use  the FP function always exclusively. It works very well.  In general, PV or PVII do not add refinement improvement on XRD pattern, but uselessy complicate the calculation

I think it is worth to stress again as Ian and Gert already mentioned. The FP approach is the only method from the options you mentioned to do quite reasonable state-of-the-art (line profile standard free) microstructure analysis ! In fact I think it is one of the exclusive selling points for TOPAS.