One difference is that four-sampler analyzers can do true TRL calibration. Three-sampler analyzers are usually built to reduce cost or size of the analyzer.
Dan is correct, in a way, about true trl. More generally, there are classes of calibration techniques which assume an 8 term error model, that can be solved most easily with 4 receivers (we don't use samplers on any of the modern network analyzers). These include TRL, TRM, SOLR (unknown thru), QSOLT among others.
However, with Rev 6 of the PNA firmware, we support a function called "delta-match" cal, with uses a previous 12-term cal to characterize the difference between source and load match (which is usually done by the 4th receiver), which then allows us to do a true TRL cal using only 3 receivers. It is somewhat (thought truely not directly) related to two-tier calibrations.
However, with Rev 6 of the PNA firmware, we support a function called "delta-match" cal, with uses a previous 12-term cal to characterize the difference between source and load match (which is usually done by the 4th receiver), which then allows us to do a true TRL cal using only 3 receivers. It is somewhat (thought truely not directly) related to two-tier calibrations.