Your best solution might to set 2 ranges, each taking values from tables in Sheet1 and Sheet2. Let's call them rgSrcTable and rgDestTable. Then you need to loop using For Each through each range and compare top and left headers, and when you find a match, copy the value of the cell in rgSrcTable to the cell in rgDestTable.

Edit: Code sample. Feel free to adapt ranges to your needs. Since this routine used Range.Value property, you can filter any data (string, numbers, etc.)

Option Explicit

Sub CopyDataWithFilter()
    Dim iRowHeader As Integer, iColHeader As Integer
    Dim rngSrc As Range, rngDest As Range, celSrc As Range, celDest As Range
    
    iRowHeader = 2
    iColHeader = 1
    With ThisWorkbook
        ' Set source and destination ranges. Modify ranges according to your needs
        Set rngSrc = .Worksheets("shtSrc").Range("$B$3:$E$5")
        Set rngDest = .Worksheets("shtDest").Range("$B$3:$E$5")
        
        ' Loop through source range and dest range
        For Each celDest In rngDest
            For Each celSrc In rngSrc
            
                ' Compare top headers and left headers respectively. If matching, copy the value in destination table.
                If .Worksheets("shtSrc").Cells(celSrc.Row, iColHeader).Value = .Worksheets("shtDest").Cells(celDest.Row, iColHeader).Value And _
                   .Worksheets("shtSrc").Cells(iRowHeader, celSrc.Column).Value = .Worksheets("shtDest").Cells(iRowHeader, celDest.Column).Value Then
                   celDest.Value = celSrc.Value
                End If
            Next celSrc
        Next celDest
    End With
End Sub

Result: