VBA code that compares 2 sheets from different systems
You turn off ScreenUpdating and Calculation and never turn them back on. Make sure you do that.

Application.ScreenUpdating = False
Application.Calculation = xlCalculationManual


You have your variables but the names can be improved. Variable names that describe what your code is doing will make it easier when you or whomever inherits the workbook after you has to edit it later. Declare them just before you use them, ws4 is not used anywhere and can be removed.

    Dim ws1 As Worksheet, ws2 As Worksheet, ws3 As Worksheet, ws4 As Worksheet
    Dim i As Long, j As Long, iCol As Long, iRow As Long, sl1 as Long, sl2 as Long


You're looping through rows and looking at columns using magic numbers (1, 2, 3, 17, 24) that have some meaning. I've no clue why any of them are important. Give a descriptive constant that tells you what it's there for.

Best I can discern you don't want something else done. Remove it.

If ... Then
    'SomeCode
Else
End If


Much cleaner. No "guessing" if an Else was forgotten

If ... Then
    'SomeCode
End If


You check for certain criteria before populating. Create a function for that and allow that to be your check. 

If Trim(ws1.Cells(i, 1).Value2) = Trim(ws2.Cells(j, 1).Value2) Then
    If Trim(ws1.Cells(i, 17).Value2) &lt;&gt; Trim(ws2.Cells(j, 24).Value2) Then 'this is the criteria so if different.


Becomes. You now focus on providing what's needed for the function to return it's Boolean (True/False) instead of how it's doing it.

If IsDataValidForPopulation(primarySheet, primarySheetRow, secondarySheet, secondarySheetRow) Then


Below is the body of the function. Trim was replaced with Trim$ to avoid 
an implicit conversion.

Private Function IsDataValidForPopulation(ByVal primarySheet As Worksheet, ByVal primarySheetRow As Long, ByVal secondarySheet As Worksheet, secondarySheetRow As Long) As Boolean
    Const PRIMARY_SHEET_CRITERIA_COLUMN As Long = 17
    Const SECONDARY_SHEET_CRITERIA_COLUMN As Long = 24

    If Trim$(primarySheet.Cells(primarySheetRow, 1).Value2) = Trim$(secondarySheet.Cells(secondarySheetRow, 1).Value2) Then
        If Trim$(primarySheet.Cells(primarySheetRow, PRIMARY_SHEET_CRITERIA_COLUMN).Value2) &lt;&gt; Trim$(secondarySheet.Cells(secondarySheetRow, SECONDARY_SHEET_CRITERIA_COLUMN).Value2) Then
            IsDataValidForPopulation = True
        End If
    End If
End Function


Your population is next. The name PopulateData describes what's being done, the parameters populationSheet, populationRow, and populationColumn also self document. You were incrementing iCol several times iCol = iCol + 1 and then set it back at the end. That's been replaced and eliminates the vertical scrolling. Note: the ByRef on populationRow. This allows the incrementation done at the end to be seen by the caller and continue offsetting to the next row.

Private Sub PopulateData(ByVal primarySheet As Worksheet, ByVal primarySheetRow As Long, ByVal secondarySheet As Worksheet, ByVal secondarySheetRow As Long, ByVal populationSheet As Worksheet, ByRef populationRow As Long, ByVal populationColumn As Long)
    'Describe your magic numbers. Rename them appropriately
    Const FIRST_NUMBER As Long = 1
    Const SECOND_NUMBER As Long = 2
    Const THIRD_NUMBER As Long = 3
    Const FORTH_NUMBER As Long = 17
    Const FIFTH_NUMBER As Long = 24
    With populationSheet
        .Cells(populationRow, populationColumn).Value2 = primarySheet.Cells(primarySheetRow, FIRST_NUMBER).Value2
        .Cells(populationRow, populationColumn + 1).Value2 = primarySheet.Cells(primarySheetRow, SECOND_NUMBER).Value2
        .Cells(populationRow, populationColumn + 2).Value2 = primarySheet.Cells(primarySheetRow, THIRD_NUMBER).Value2
        .Cells(populationRow, populationColumn + 3).Value2 = primarySheet.Cells(primarySheetRow, FORTH_NUMBER).Value2
        .Cells(populationRow, populationColumn + 4).Value2 = secondarySheet.Cells(secondarySheetRow, FIFTH_NUMBER).Value2
    End With

    populationRow = populationRow + 1
End Sub


You had Set ws3 = ActiveWorkbook.Sheets("NINO Differences")' this will be a different sheet as I change the criteria which meant you'd need to change the code. Through refactoring and using the parameter populationSheet you now mandate that whoever calls this Sub needs to supply the required sheets.

Private Sub NINODifferences(ByVal primarySheet As Worksheet, ByVal secondarySheet As Worksheet, ByVal populationSheet As Worksheet)

    Application.ScreenUpdating = False
    Application.Calculation = xlCalculationManual

    Dim primarySheetLastRow As Long
    primarySheetLastRow = primarySheet.Cells(primarySheet.Rows.Count, 1).End(xlUp).Row

    Dim secondarySheetLastRow As Long
    secondarySheetLastRow = secondarySheet.Cells(secondarySheet.Rows.Count, 1).End(xlUp).Row

    Const populationColumn As Long = 1
    Dim populationRow As Long
    populationRow = 2

    Dim primarySheetRow As Long
    Dim secondarySheetRow As Long
    For primarySheetRow = 1 To primarySheetLastRow
        For secondarySheetRow = 1 To secondarySheetLastRow
            If IsDataValidForPopulation(primarySheet, primarySheetRow, secondarySheet, secondarySheetRow) Then
                PopulateData primarySheet, primarySheetRow, secondarySheet, secondarySheetRow, populationSheet, populationRow, populationColumn
            End If
        Next secondarySheetRow
    Next primarySheetRow

    Application.ScreenUpdating = True
    Application.Calculation = xlCalculationAutomatic

End Sub


You now have the option to create something like what follows to provide the sheets you need it run on. Note: I suggest renaming the Worksheets.CodeName member do be descriptive and use that in place of ActiveWorkbook.Sheets("SheetA") since you're using the name displayed on the sheet tab. If that get's changed you'll have to change your code.

Public Sub Test()
    Dim ws1 As Worksheet
    Dim ws2 As Worksheet
    Set ws1 = ActiveWorkbook.Sheets("SheetA") 'Use the Worksheet.CodeName member

    Set ws2 = ActiveWorkbook.Sheets("SheetB")
    NINODifferences ws1, ws2, ActiveWorkbook.Sheets("NINO Differences")
    NINODifferences ws1, ws2, ActiveWorkbook.Sheets("FOO Differences")
    NINODifferences ws1, ws2, ActiveWorkbook.Sheets("BAR Differences")
    NINODifferences ws1, ws2, ActiveWorkbook.Sheets("DUK Differences")
    '...
    NINODifferences ws1, ws2, ActiveWorkbook.Sheets("ZZZ Differences")
End Sub