The number of IF stages is important to be sure, but all the "extra" IF stages provided beyond those needed for basic amplification duties (typically two) are there to improve the selectivity of a given design, and the ability for the limiter to fully function on the weakest signals.
Also, the tubes used make a difference as well. The early version 400 receivers used only a three tube IF strip, one of which was a 6HS6, which is a high Gm tube. In later versions, Fisher converted to a four tube IF strip, using all 6AU6 tubes -- which are lower Gm tubes. The gain of both IF strips however, is about the same. The potential advantage of the latter design then is with improved selectivity, and possibly improved limiting action as well, but the basic performance of the two designs will largely be the same.
The 400 was a wonderful effort to achieve most of what the 500C provided in performance, but at a reduced price point. This undoubtedly led then to the original three tube IF strip design used in these receivers. But production of specialty vacuum tubes was winding down quick back in the mid 60s, since their wide spread use was quite small compared to that of main line tubes. Therefore, I believe that Fisher wisely moved to a four tube IF strip in this receiver not for improved performance, but primarily due to large scale availability concerns for "real" 6HS6 tubes. The move to use more main stream tubes then (and the resulting extra IF stage), was likely a stopgap measure to allow continued production of the 400 receiver, with performance credentials that the company could still stand behind, at a time when it was quickly moving to change over to the new SS format.
Dave