RichCopy. Better than the command-line Robocopy and better than Robocopy with the GUI addon. RichCopy is a newer replacement generally accepted as the evolution of Microsoft copying tools. It's multi-threaded so it'll copy multiple files in parallel. Progress can be paused and resumed and it'll handle network interruptions. Furthermore, settings are very granular. You can select when to copy if the file already exists based on modification date, filesize, and other attributes. Give it a try and let us know if it preserves timestamps of nested directories. That link is a blog post introduction but the program is downloaded from a link at the top.
The author of RichCopy is Ken Tamaru and he posts occasional information and updates at his blog.