When comparing 7-Zip vs TeraCopy, the Slant community recommends 7-Zip for most people. In the question“What are the best archiving tools for a data hoarder?” 7-Zip is ranked 1st while TeraCopy is ranked 5th. The most important reason people chose 7-Zip is:
7-Zip is licensed under GNU LGPL, and the *.7z format has support across all major operating systems. There should be no trouble opening the archives under any operating system, and no need to deal with messages bugging you to register or pay for the app. Source code can be found [here](http://www.7-zip.org/download.html).
Specs
Ranked in these QuestionsQuestion Ranking
Pros

Pro Free and open source
7-Zip is licensed under GNU LGPL, and the *.7z format has support across all major operating systems. There should be no trouble opening the archives under any operating system, and no need to deal with messages bugging you to register or pay for the app. Source code can be found here.

Pro High compression .7z format
Their own file format .7z that ships with 7-Zip is one of the best compression formats. 7z file format is usually more compact than Zip.
Pro Lightweight
Starts quickly.
Pro Explorer right-click menu integration
Makes it easy to open any archive file, or create new archives, without having to go open another program first.
Pro Very fast compression/decompression
7z is muli-threaded, allowing it to do very fast compression and decompression.
Pro Unobtrusive
No nag screen.
Pro Faster file deletion
It deletes files much much faster than built in Windows file manager.
Pro Can check files for copy errors
TeraCopy can automatically check/verify the copied files for errors, by calculating their CRC or other checksum/hash value.
Pro Seamless shell integration
Pro Skips badly copied files
TeraCopy skips badly copied files during the copying process, and then displays them at the end of the transfer "Verify" with checksum/hash, so you can see which files to re-copy. See also, OpenHashTab for Windows and DeadHash for Windows, Linux, Android.
Cons
Con GUI looks dated
Could use a new fresh user interface.
Con XZ/LZMA2 format inadequate for long-term archiving
LZMA2 is unsafe and less efficient than the original LZMA. Use: 7Z LZMA Non-Solid, RAR 5 LZSS/PPMd Non-Solid, or ZIP Deflate. See here.
Con Does not support data recovery
It's not possible with 7-zip to add data recovery records to the archive which could repair minor integrity errors.
Con Sometimes clashes with 7 zip
From my experience, TeraCopy does not do well in conjunction with 7zips.
It seems to error on some systems when you do a drag-and-drop extract.
