You don't need a "mega" battery backup system for it to work. The Cyberpower PFC series range from $100.00 to $180.00 depending on which model you get. Since you already have the battery backup, why not just pick a power supply that doesn't use Active PFC, such as this Thermltake
http://www.newegg.com/Product/Product.aspx?Item=N82E16817153023
It's not weird for your BI computer to have a better CPU than your gaming computer, BI is a lot more CPU intensive than your games. So you many not need an i7 for your gaming computer, but if you're going to have 12 or more HD cameras, than you may need an i7 for your BI computer. The computer should built according to it's use, not because you don't want it to be better than your gaming computer.
I don't know where you live, but Microcenter offers great deals on Intel CPU's. Last week they had the i7 6700k for $289.00, and when you bundled it with a motherboard, they took off an additional $30.00.
Years ago I use to build computers using AMD chips, however, they have fallen behind the times. Right now they're good for budget systems, however, it's not a smart idea to use them for a BI computer. The power consumption is too high, plus you won't be able to take advantage of Intel Hardware acceleration. In my opinion Intel Hardware Acceleration is a must, especially if you have a lot of cameras on the system. It will significantly reduce you're CPU usage when enabled.
