Without knowing your OS, it's hard to say if copy/paste is sufficient - as jvb commented, you could have all sorts of problems with ACLs/ownership/whatever (though usually, that's unlikely), but it's also a reliability-issue.
I've seen Windows Explorer (from WinXP to Win10) silently aborting larger file-operations many times. I have seen the same behavior with OS X and its Finder just as many times. Ubuntu/Linux...not yet, although that's perhaps because I don't frequently move/copy files with it.
To clarify: that's not something only one computer has ever done or something that only happens with WiFi-connections or with one particular file - it's not something that happens very often, but if it does (and in my experience, the more files -> the more likely it crashes), you end up some files copied but without any information as to what happened or which files were copied without problems and which file was only half-way-finished.
Solution: Use some third-party-GUI-tool like Free Commander (FreeWare, Win)| Total Commander (ShareWare, Win) | Midnight Commander (FreeWare, *NIX), or use OS-built-in CLI-tools like Robocopy (Win) | XCopy (Win) | cat (*NIX) | ... .
Syntax is varying from tool to tool, e.g.:
robocopy d:\ f:\ /copyall /e /z /r:5 /w:15 /v
xcopy d:\ f:\ /e /c /h /k /o /x
cat /dev/sdb >/dev/sdf
sdb resemble your old 4TB-volume,
sdf your new 6TB-volume.)
Code-sources and additional information: Robocopy - XCopy - cat
I never had issues with any of these tools - however, it's always wise to double-check everything:
- At least check if all files were copied successfully by checking the file/folder-counter and the overall size,
- to avoid the possibility of damaged files (because of bit-errors) it's also wise (yet very time-consuming) to check file-hashes (MD5/SHA1 will do in this case, as we're not looking for malicious manipulations of files). Some of the tools mentioned above can do that on-the-fly when copying.