Ubuntu :: Bash Copying Files From One Drive To Another?

I've got two external hard drives, a 2TB and a 320GB. I've recently come from Windows 7. On Windows 7 I wrote a batch file which checked whether both hard drives existed and then copied a couple of folders from the 2TB to the 320GB without overwriting. I've been trying to work out how to do the same under Linux without much luck. I've tried rsync but it looks like it overwrites. Does rsync overwrite?

If it helps, the batch file I wrote in Windows

if exist D:320GBDrive (if exist H:2TBDrive (xcopy H:2TBDrive* D:320GBDrive /I/E /-Y < C:decline_copy.txt))

Which basically checks for drive D:, checks for drive H: and then copies the contents of the folder on drive H to drive D and says no every time it asks to overwrite.