the closest that you will get is the Motorola Moto G, which is considered a low-end device in contrast to the iPhone. So the price for the Moto G is much lower, but I assume you won't get the same great performance as on iOS.
There's also the HTC One Mini or the Galaxy S4 mini. Both feature a mid-range processor and over 1GB RAM. Because Samsung and HTC use their own customizations and User Interfaces I'd recommend using a custom ROM, like cyanogenmod. There is currently no official CM support for either devices, but I'm sure there are many ports available. These would offer a smoother user experience compared to the stock ROMs.
The best choice is to wait for the devices releasing early 2014. The Sony Xperia Z1S is said to arrive 2014 and this one beats all the "Mini"-Versions of other manufacturers, at least spec wise. It is said to offer a Snapdragon 800, 2GB RAM and an outstanding 20.7 megapixel camera. If price doesn't matter, what I assume when you're searching an iPhone-alternative, I'd wait for that one. I will probably consider it myself.