I have been the personnel manager of my own company for over 14 years and in total I have hired more than 70 people. I've read hundreds of resumes. I've done hundreds of job interviews. dragonchild put it quite right: I know exactly whom I will choose. I too would have chosen the person who did some work related to security.

Several other people made it clear as well. Having more than one job title on your resume makes you more interesting (and that's just talking about the job title). People that can do one thing might be interesting if they are very good. But I always wanted my programmers, system engineers and system operators to be at least a bit versatile. At least a bit of this and a bit of that. They have to prove to me they have learned how to learn. Flexibility. Being eager to do something new. Surprising.

Once I turned down somebody who worked as a Unix, C and Oracle programmer his whole adult life, creating and maintaining financial systems. Even though he has made some very nice programs. But he could not tell me that he has done some other things, like setting up and maintaining servers, working with more than one database system, working with networks and security, trying to learn other programming languages, because he never gave it much of a try. He understood my point, and asked me if he could proof his quality to me. Of course I agreed. Three months later he visited me again. He had learned more than the basics of Perl and MySQl (and a bit of Linux, Apache and sendmail) and made a database-driven website for me, with a small web shop. Basic, rudimentary, but impressive nontheless. I hired the guy and he turned out to be a wonderful colleague.

Your current job might be nice and safe. You're probably good at what you do. The least you could do is broaden your horizon. if you're not going to take the other job, invest in yourself and learn in your own time about security and other interesting things. And try to apply your knowledge in your job. Who knows what it will bring you.