A key point users will need to come to terms with is that LOD expressions are not just a new form of table calculations. Technically they operate quite differently and although there is some overlap in the problems they can solve there is generally a clear line in determining which to use. The following table shows how the two types of calculation differ:
Table Calculations  LOD Expressions  
Table calculations are generated from the query results.
WINDOW_AVG(SUM([Sales])) 
LOD expressions are generated as part of the query to the underlying data source. They are expressed as a nested select so are dependent on DBMS performance:
SELECT T1.[State],SUM(T2.[Sales per County, State]) 

Table calculations can only produce results that are less granular than the Viz LOD.  LOD expressions can produce results that are more granular than, less granular than or totally independent of the Viz LOD.  
Dimensions that control the operation of a table calculation are separate from the calculation syntax and specified in the “compute using” or “running along” menus.  Dimensions that control the calculation for a LOD expression are embedded in the calculation syntax. For INCLUDE and EXCLUDE expressions these are relative to the Viz LOD, for FIXED expressions these are absolute.  
Table calculations are always aggregated measures.  Calculated fields with LOD expressions can be measures, aggregated measures or dimensions. INCLUDE/EXCLUDE expressions are always measures or aggregated measures. FIXED expressions are dimensions by default but can also be used as measures.  
Table calculations cannot be used in other constructs.  LOD expressions can be used in other constructs such as bins, groups, etc.  
Filters on table calculations act as a hide – they do not remove records from the result set.  Filters on LOD expressions act as an exclude – they remove records from the result set. Depending on whether the expression is FIXED or INCLUDE/EXCLUDE it is evaluated at different stages of the visualisation pipeline. 
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Very helpful! Thanks for compiling these comparisons.
Great series Alan! Definitely helpful for me to wrap my mind around LoD expressions. Thanks!