That's like asking which car is better? A Nissan or a Toyota?
There is no one that is better than the other. That is an unfair question to ask others, and should be determined on a case-by-case basis.
No, BSD is not any more secure than a Linux box. OpenBSD (one of the BSD folks) has prided itself in not shipping a OS that is insecure remotely out of the box, but the biggest part of that security is that they just don't have anything run by default. You could that on most boxes, unless you wanted to use them for something.
If you want to compare them, either download a BSD variant and a Linux variant and put them head to head and see what you think. If you don't have the bandwidth to download all that software, head on over to www.cheapbytes.com
and order some cheap software. I've had good experiences with them.