In fit curve there is an option to display a parameter estimates table. The table uses a Group role to present the table of statistics.
In fit model, to get something similar the user is required to go to first turn on multiple non-default columns, then make combined data table, then split the table, then repeat this for the fit statistics and concatenate the tables. This is a lot of steps and the action recorder doesn't pick them all up, so easy workflow scripting isn't possible. (for example, right-click on column, turn on Upper and lower CI for intercept and slope.)
in Fit Model, it would be nice if there were a parameter estimates summary table that included fit statistics and parameter estimates for each level of the By variable.
In Fit curve, it would be nice if the fit statistics were available in the summary table for each Group level, in addition to the parameter estimates.