Which is better in terms of performance & memory usage, which is
higher performance and less memory usage?

"Select Case" VS "Elseif" 

The language I am asking about is VB6.

I don't believe there is a noticeable difference with today?s systems,
the main difference how easy it is to read the code.  Select case us
much less cluttered if you have several cases to work with.

One thing to note however, is the following:

A switch statement only needs to evaluate once, while if you have
multiple if statments
asking the same thing, they have to evaluate more than once. For example:

Select Case 1 + 3
    Case 1:
        MsgBox "1"
    Case 2:
        MsgBox "2"
    Case 3:
        MsgBox "3"
    Case 4:
        MsgBox "4"
    Case Default:
        MsgBox "Default"
End Select
If 1 + 3 = 1 Then
    MsgBox "1"
ElseIf 1 + 3 = 2 Then
    MsgBox "2"
ElseIf 1 + 3 = 3 Then
    MsgBox "3"
ElseIf 1 + 3 = 4 Then
    MsgBox "4"
End If

The select case only had to evaluate 1+3 once while the if had to do it 4 times.