If the old drive held any personal info, for example bank details, passwords etc. then it would be well worth making sure that all the data is properly deleted. A format doesn't do that, it merely over writes the file allocation table, so that all the data is still there, and recoverable with freely available software.
You can get hold of free software to ensure that all such sensitive data is effectively destroyed, barring a full and expensive forensic search of the areas between the tracks on the disk.
This software:-
Eraser
does the job nicely, although it will take some time depending on the size of the disk and number of overwrites selected. For a basic level of protection against software recovery one pass should be sufficient.