I appreciate all the answers, received here and in private, explaining some of the mechanics behind the discrepancy in DNA match data from MyHeritage and Ancestry.  It seems that the majority of responses report that MyHeritage combine smaller segments and includes questionable segments, inflating their totals.  Ancestry, on the other hand, eliminates smaller segments, pile-up areas and other questionable segments, to provide a more conservative (and realistic?) report, according to these responses.   Many suggested comparing matches on GEDMatch as a more reliable platform.

As it turns out, I have collected match data from several different sources into a table, so I decided to check into this.  I don't have a lot of instances where someone tested on MyHeritage and Ancestry to be a representative sample, but I thought this was a start.

Karen           total       #         largest
Ancestry       110       11           22
GedMatch     110                      22

Mildred*          total       #         largest
MyHeritage    124        6           31.7
GedM             126.4                  29.7

Robert*           total       #         largest
An                   168        16         28
GedM              155.8                 29.3

Jane                 total       #         largest
MH                   664.6      20        110.3
FTDNA             656         16        119.75

Linda                  total       #         largest
An                      124        16          18
FTDNA               116        12          21

G.A.                    total       #         largest
An                        172       14          27
MH                       146.2    10         25.5

Mike *                 total       #         largest
An                        168       9          72
MH                       148       7          69.9
GM                       155.7               47.1

Penny *               total        #         largest
An                       179        14          41
MH                      174.7     13         32.4
GM                      153.5                  38.1

Janet **                 total       #         largest
MH                        350.9    17         60.2
FT                          363        16         66 

Alan **                   total       #         largest
An                          598       15          67
MH                         590.7    18         109.1
  
Nancy *                  total       #         largest
FT                             83       6            36
GM                           82.7                  24.6

* known 3rd cousin
** known 2nd cousin

From this small sample, I don't see a pattern that makes a case that Ancestry is more conservative or MyHeritage inflates its reports.  MyHeritage's numbers are close to and sometimes lower than Ancestry's.  MyHeritage's numbers are also consistent with GEDMatch and FamilyTreeDNA in the few cases where 3rd party comparisons were available.  I definitely don't see anything here that would explain a 4x discrepancy in the two match reports I posted originally.  Does anyone have another explanation?

Lee David Jaffe
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Surnames / Towns:  Jaffe / Suchowola, Poland ; Stein (Sztejnsapir) / Bialystok and Rajgrod ; Roterozen / Rajgrod ; Joroff (Jaroff, Zarov) / Chernigov, Ukraine ; Schwartz (Schwarzstein) / Ternivka, Ukraine ;  Weinblatt / Brooklyn, Perth Amboy, NJ ; Koshkin / Snovsk, Ukraine ; Rappoport / ? ; Braun / Wizajny, Suwalki,  Ludwinowski / Wizajny, Suwalki