It's best if you think of it that way rather than as a smaller version of Samsung's flagship Galaxy S4 device. Despite its name, the S4 mini isn't really just miniaturized S4, and if that's what you were expecting, you're going to be disappointed.
On its own, the S4 mini is a respectable budget phone. It has a 4.3-inch qHD Super AMOLED display, 1.7GHz dual-core processor, 1.5GB of RAM, 8GB of internal storage, 8MP rear-facing camera, 1.9MP front-facing camera, microSD card slot, 4G LTE connectivity, built-in Wi-Fi and Bluetooth, 1,900mAh battery, and Android 4.2.2 Jelly Bean. It measures 124.6 x 61.3 x 8.94mm and weighs 107g.
How does that compare to the popular S4? Samsung's flagship device wields a 5-inch Full HD 1080p Super AMOLED display, 1.9GHZ quad-core processor, 2GB of RAM, 16GB/32GB internal storage, 13MP front-facing camera, and 2MP rear-facing camera, to cover some of the main differences.
It's not really fair to compare the two in a head-to-head match-up since they're targeting two different market segments at presumably two different price points (Samsung hasn't yet said how much the S4 mini will cost), though comparisons are inevitable given the device's name.