I just graduated with a double major in CS and Math (pure Math, not Stats). I think you first need to figure out exactly what it is you want to do as a career. I know it takes a long time to figure this out, trust me, I changed majors seven times. If you are really torn between CS and Stats, then I would do a double major. So what if it takes 1-2 years longer. You will actually ENJOY your job one day. I would NEVER decide what to major in based on how fast you can be done with school. Then you will graduate and be completely miserable in your job the rest of your life.
Now some thoughts of mine between Stats and CS. First of all, I hate Stats with a passion, I find it completely mind-numbingly boring, so I may be slightly biased. But Stats majors can find some pretty successful jobs. If you see yourself being happy sitting in front of a computer crunching numbers (and yes, of course, going to the occasional meeting, etc.), then Stats will be good for you. CS on the other hand, while it presents a similar working environment, lets you be a little more creative and intellectual in your profession. To me, this is something I absolutely need in a job. Currently, I am working at a company doing some probability work along with a lot of coding. I really enjoy the mix. I have found that having both CS and Math under your belt is A LOT better looking to employers than just one or the other, and it also makes your job a lot more fun.
I am also curious why you havent taken many CS classes. Have you just been taking light loads? If I were you, I would do a double major, and if along the way you strongly feel you like one more than the other, then go that route. But don't force yourself to decide now just to save time. That is my advice anyway. I became a double major at the end of my junior year, and so I was in college as an undergrad for 5.5 years. But let me tell you, I worked hard and got what I wanted, and I don't regret it at all. I will be starting a PhD program in Math this semester, and so I am leaving CS behind. But I plan on keeping up with it because it is something I really enjoy.
In regards to job security, I think CS and Stats are pretty similar, and I certainly wouldnt let that be the deciding factor. Anyway, hope this helps. Let me know what you think :)