Apple's Migration Assistant is convenient for transferring over all of your web bookmarks, Mail, and computer settings but it is always a good idea to re-install your software on new computers. Not all of the support files are transferred over.
The activation system creates license files tied to a computer's hardware. If you get a new computer, you will need to activate it before using the software - your old computer's activation file will cause errors on your new Mac when trying to open the software, as it was created based on different hardware.
If you are going to stop using the old computer, be sure to de-activate it in order to not lose an activation.
If you have already transfered your files from the old computer using Apple's Migration Assistant, you will need to delete the old activation file before you are able to activate your software on the new computer. The license files are located at:
Mac HD>Library>Application Support>Soundness>Licenses
For BIAS products:
Mac HD>Library>Application Support>BIAS>Licenses