I moved files to obtain available space to reinstall OS, and thus none files left behind on the old hard drive.
But, as I mentioned I was not promted to accept formatting of the disk. After having googled "file recover software mac" I found a program called Disk Drill. After having used this for 2 hours it located and restored 62 out of 69 gb, and I am very pleased. My assumption was correct in the way that it was hard to believe that the files was deleted.
Posting the problem here led to a solution and for that I am thankful.
Another question. What are the reasons for choosing one file-system instead of another apart from the fact that Exfat enables understandable language for both mac and pc.
Mac OS extended (journaled)
Mac OS extended (journaled, encrypted)
Mac OS extended (case sensitive, journaled)
Mac OS extended (case sensitive, journaled, encrypted)
MS-DOS FAT
ExFAT
Windows NT filesystem (tuxera NTFS)
Windows NT filesystem (NTFS 3G)