In my tests, Choose took more than 22 times as long as Select Case. Select Case took about twice as long as the array assignment.

Private Sub btnGo_Click(ByVal sender As System.Object, _
    ByVal e As System.EventArgs) Handles btnGo.Click
    Dim start_time As DateTime
    Dim stop_time As DateTime
    Dim num_trials As Long = Long.Parse(txtNumTrials.Text)
    Dim ellapsed_time As TimeSpan
    Dim a As Long

    lblChoose.Text = ""
    lblSelectCase.Text = ""
    Application.DoEvents()

    start_time = Now
    for i as integer  = 1 to num_trials
        a = Choose(1 + i Mod 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, _
            10)
    Next i
    stop_time = Now
    ellapsed_time = stop_time.Subtract(start_time)
    lblChoose.Text = _
        ellapsed_time.TotalSeconds().ToString("0.00") & " " & _
        "seconds"

    start_time = Now
    For i As Integer = 1 To num_trials
        Select Case 1 + i Mod 10
            Case 1
                a = 1
            Case 2
                a = 2
            Case 3
                a = 3
            Case 4
                a = 4
            Case 5
                a = 5
            Case 6
                a = 6
            Case 7
                a = 7
            Case 8
                a = 8
            Case 9
                a = 9
            Case 10
                a = 10
        End Select
    Next i
    stop_time = Now
    ellapsed_time = stop_time.Subtract(start_time)
    lblSelectCase.Text = _
        ellapsed_time.TotalSeconds().ToString("0.00") & " " & _
        "seconds"

    Dim values() As Long = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
    start_time = Now
    For i As Integer = 1 To num_trials
        a = values(i Mod 10)
    Next i
    stop_time = Now
    ellapsed_time = stop_time.Subtract(start_time)
    lblArray.Text = _
        ellapsed_time.TotalSeconds().ToString("0.00") & " " & _
        "seconds"
End Sub