What do you mean by UNIX? Unless I'm wrong, Linux, FreeBSD, OpenBSD, Mac OS X and all others are covered under the 'umbrella' of UNIX, which was a multi-user operating system developed at Bell Labs. All those are projects that stemmed from the original creation of UNIX.
You can't really compare UNIX and Linux. Again, I'm not an authority on the subject so I'm sure someone will be along to chastise me
Linux is not Unix.
Unix was first written by AT&T long time ago.
Linux its a more recent project that was written from scratch copying unix.
To answer your question.
Unix beeing an older system its a much more stable OS and it has greater
Linux instead has a bigger user base and it supports a variety of hardware which Unix doesn't.
The general thought is that you should go with the one you're familiar with.