TeraCopy is about the same as Windows' robocopy in speed, but it does lots more of what you don't need and it hooks into the system in non-obvious ways. The only real benefit is that it has GUI while
robocopy is command-line and it may overwhelm a bit with all its options.
But fear not, here's all you need -
robocopy X:\ Z:\Backup-of-X\ /MIR /Z /FFT
X:\ is your external drive you are backing up and
Z:\Backup-of-X\ is a directory where you want the backup to go.
/MIR tells it to create an exact copy of the tree, i.e. remove files from the backup that don't exist at the source.
/Z enables resumable copying of large files, so you can Ctrl-C robocopy half way through a large file and it will start copying from the second half on the next run.
/FTT tells it to assume 2-second timestamp resolution. This has to do with how robocopy detects which files have changed and which haven't. It's a long story, just use