Miglyol 840 and 812 are both forms of MCT oil. MCT is just short for medium chain triglyceride and it's a general term for any oil that fits this criteria, including Mig 840 and Mig 812. There's no guarantee that either of the Miglyols will give you less PIP because PIP can be caused by many things and those factors vary person-to-person. However the vast majority of users do report significantly less PIP with either Miglyol form, likely due to the fact that it's much thinner than most traditional oils, and the fact that it holds a solution much better as well so you can use less solvents which are known to cause pain and inflammation (PIP).
Lastly Miglyol is nice because it's hypoallergenic so no need to worry about allergic reactions of any kind.