IPhone 4 iCloud restore from iOS 7?

I have lost my old iPhone 4 iOS 7 and had it backed up to iCloud Wi-Fi. I have a new iPhone 4 and it's currently running iOS 6.1.3 and I would like to keep it this way because I like the layout much better and it runs faster with the iPhone 4. I tried to restore my old iPhone backup but it said I can't because I had iOS 7 on that backup. I need ways to get my backup to my new phone without updating to iOS 7.

Unfortunately, it will update itself to the latest software your phone is compatible with. The same thing happened to me when I had an iPhone 4 and iOS 7 had just come out. I hated the new look but when my phone randomly decided to delete everything and I had to restore it, I ended up also getting iOS 7. I didn't like it at all either but you'll get used to it, it looks pretty cool after a while.

May be its not possible.