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The most relevant definition that the previous commands display is

Self : DeleteDuplicatesBy[expr_, f_] := 
 Module[{r$}, 
  r$ = Which[! 
     Quiet[TrueQ[! AtomQ[expr] || AssociationQ[expr] || 
        Head[expr] === SparseArray]], 
    Message[DeleteDuplicatesBy::normal, 1, "HoldForm"[Self]]; 
    Macros`$FailRHS, True, 
    Macros`HoldSequence[
     Which[ListQ[expr], Values[GroupBy[expr, f, First]], 
      AssociationQ[expr], 
      Association[Values[GroupBy[Normal[expr], f@*Last, First]]], 
      Head[expr] === SparseArray, 
      DeleteDuplicates[expr, f[#1] === f[#2] &], True, 
      expr[[Values[
         GroupBy[Table[{f[expr[[i]]], i}, {i, Length[expr]}], First, 
          First]][[All, 2]]]]]]]; 
  Macros`ReleaseHoldSequence[r$] /; ! 
    MatchQ[r$, 
     Macros`$FailRHS | Macros`HoldSequence[Macros`$FailRHS]]]

If we predict where we will end up for a list, this basically says

If we predict where we will end up for a list, the definition basically says

The behavior described here is the same from 10.0.0 up to at least 10.1.0, with the minor exception of IndexBy.

Let's see what the definition of DeleteDuplicatesBy is. This can be seen by evaluating the following code

DeleteDuplicatesBy (*to autoload some stuff*)
ClearAttributes[DeleteDuplicatesBy, ReadProtected]
oldCP = $ContextPath; (*all context stuff is just to make things more readable*)
$ContextPath = 
 Join[$ContextPath, {"Macros`Evaluation`PackagePrivate`", 
   "GeneralUtilities`System`PackagePrivate`"}]
DeleteDuplicatesBy // Information
$ContextPath = oldCP

Or in v10.1.0 this may be done conveniently by using

In version 10.0.0, the undocumented System` function IndexBy also does not work with held expressions. It also doesn't give a message when the first argument is bad but still applies some rules.

In version 10.1.0 IndexBy does not seem to do anything anymore. Curiously BenchmarkPlot still depends on that function. This causes BenchmarkPlot to fail for some inputs, including for the inputs given in Mr.Wizard's answer.

The behavior described here is the same from 10.0.0 up to at least 10.3.

Let's see what the definition of DeleteDuplicatesBy is. From v10.1.0 onwards, this may be done conveniently by using

The behavior described here is the same from 10.0.0 up to at least 10.1.0.

The undocumented System` function IndexBy also does not work with held expressions. It also doesn't give a message when the first argument is bad but still applies some rules.

The behavior described here is the same from 10.0.0 up to at least 10.1.0, with the minor exception of IndexBy.

In version 10.0.0, the undocumented System` function IndexBy also does not work with held expressions. It also doesn't give a message when the first argument is bad but still applies some rules.

In version 10.1.0 IndexBy does not seem to do anything anymore. Curiously BenchmarkPlot still depends on that function. This causes BenchmarkPlot to fail for some inputs, including for the inputs given in Mr.Wizard's answer.