In Office 2003, which I use, the only way (I think) of doing what you want to do is to open up Excel, choose the file you want to open, then open Excel again, and open the file you want to see side by side. Double clicking on a file in Explorer just causes that file to be opened as a new window in the copy of Excel that's running. You have to 'force' Windows to open two copies of Excel.
Ah - Lotvic's response has made me realise that what I was talking about was when you're in a dual screen environment, and you want one spreadsheet open on one screen and another open on another screen...
I have just read your post and like Ian in Northampton, I use Office 2003. There if you have two or more spreadsheets open, click on 'Window' at the top and then make sure you get the full drop down list. One of the options is 'Compare side by side with..' which gives you the option to choose which spreadsheets you want to compare.
Do this to view different worksheets in the same Workbook: Open your workbook in Excel > click on 'Window' to get the dropdown menu, > click on 'New Window', you now have the same workbook open twice
again click on 'Window', to get the dropdown menu > click on 'Arrange' > choose 'Vertical' and click on 'OK'. You can now look at two different worksheets from the same workbook (click on the sheet tabs at bottom). Each view will work independent of the other when you scroll up and down the worksheet. You can close one instance of the Workbook and the other will still be open and displayed.
Do this to view different Workbooks: Open Workbook1. > Open Workbook2. > click on 'Window', to get the dropdown menu > click on 'Arrange' > choose 'Vertical' and click on 'OK'. You can now look at two different Workbooks and if you close Workbook1. then Workbook2. will still be open and displayed.
If you choose 'Compare side by side' when you scroll your mouse button both of the Worksheets on view will move up and down together - not independently.
I saw your reply to me, and I don't know why you don't have 'Compare', but I have usually 4 or 5 spreadsheets open, so I clicked on arrange and they all appeared on the screen!! If you are happy - especially as it works for you - stay with lotvic's advice, but I think it might be of help to you.