Why not use both ?
Sure I'd consider BSD for a server application which needs to run on a virtual machine for years without hassle, so long as it didn't have too many dependencies I had to compile and fix the source code for. That's where the package system which keeps the convoy of supported applications compatible with each other together, and that comes with the OS, is crucial to whether or not it's the right tool for the job.
Before good package systems, a lot could be achieved by compiling stuff from source code, but nowadays that can all too easily result in dependency hell and a lot of bug fixing.
Just about any OS and it's supported software packages will come to end of security supported life at some point where your choice is to let the application you've built on it continue until someone breaks it, or to rebuild it on something newer which does have security support. Using the OS's self upgrade mechanism doesn't always upgrade all the application dependencies - sometimes these are left installed and running but lose security support themselves.
There's also probably greater differences between different Linux flavours including embedded versions running on matchbox sized routers with tiny amounts of memory, than between server versions of Linux and BSD.