When comparing The Unlicense vs Simplified BSD License, the Slant community recommends Simplified BSD License for most people. In the question“What are the best open-source licenses?” Simplified BSD License is ranked 5th while The Unlicense is ranked 10th. The most important reason people chose Simplified BSD License is:
BSD licensed software can be used with proprietary software.
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Pros

Pro Removes any possible licensing issues
Everything under the Unlicense is part of the public domain, which means that anything can be done with it.
Pro Protects the author
The author of the software avoids any risk for how the software may be used by others.
Pro Unlicensed code is easy to find
When using public code hosts such as GitHub and BitBucket it is suggested to use the filename UNLICENSE instead of the more traditional LICENSE or COPYRIGHT to store the license so it's easier to find unlicensed code. Additionally, the first line of the license is worded in a unique way specifically to allow searching for it with search engines.
Pro Short and simple
The Unlicense is just 3 paragraphs long.
Pro Can be used with proprietary software
BSD licensed software can be used with proprietary software.
Pro Short and simple text
This license has one requirement with 2 clauses, both of whcih are related to the distribution of the license itself.
Pro Protects the author
The author of the software avoids any risk for how the software may be used by others.
Pro Prevents lock-in
The license basically allows anyone to do whatever they want with the code as long as the original copyright and license notice is included along with the copy of the code. The code can be used for commercially, it can be modified and it can be distributed.
Cons

Con Hasn't been reviewed by OSI
The OSI (Open Source Initiative) is an organization that promotes open source software and they commonly review open source licenses. However, they have decided not to review Unlicensed because it has not been written by legal professionals.
Con Gives no control of how the code is used
Putting the code in the public domain leaves it open to abuse.
Con Nothing prevents someone else from making money off of your software
The 2-clause BSD license is permissive enough that anyone can take your code, rebrand it and sell it.