You won't get a useful answer without
a. finding someone who is running (or has run) the exact same work load on both OSes on the same hardware
or
b. benchmarking it yourself in test. work out your application's bottleneck(s) and test both platforms for it on your hardware before making the choice.
However, comparing on performance out of the box only is only somewhat useful. Both platforms can be tuned, both platforms will no doubt have hardware and workloads that they are best at, and both platforms running on appropriate hardware are likely to be plenty fast enough. I suspect competence of your admin will have more of an effect on performance than the OS of choice.
FreeBSD can run SOME Linux applications faster than Linux, but this was measured years ago (back in the Linux kernel 2.0 days - may or may not hold true today, and can't run 64 bit Linux apps), and isn't true for all applications in any case.
Additionally, some commercial applications are only supported on Linux.
Work out what your requirements are, do a pro/con on both options and make your choice. I suspect performance difference when both are configured properly will be negligible (also, FreeBSD has traditionally been more responsive under load which may or may not be important to your application); the more important differentiators are how good your admin is (if you have a Linux-only admin available he'll be crap at FreeBSD and vice versa), what level of commercial application support you need, what hardware support you need and whether or not there are any other features available in one OS but not the other that are of importance to you (e.g., DTrace, ZFS, Beowulf clustering, etc).
I've run both Linux and FreeBSD over the years, and prefer BSD due to the more stable user land (in terms of breaking compatibility), better response under load and being more true to the "unix way" of doing things.
But... I have a couple of RHEL boxes at work (barf). Why? Because our application is only supported on Solaris, SCO or RHEL.