The answer is simply.. no. The S4 Mini is not a mini version of the S4, it's a completely different and much less powerful handset. Although the specifications of the "Mini" are not bad, they are in no way close to the fully-blown S4. Yes, its about 25% lighter and has a 20% smaller footprint, so it's definitely not as massive as the S4, but that really is about all it has going for it.
A quick look at the comparison table below shows just how far off the Mini is:
|Samsung Galaxy S4 Mini||Samsung Galaxy S4|
|Screen resolution||540 x 960||1080 x 1920|
|CPU||1.7GHz dual-core||1.9GHz quad-core|
|Internal storage||8GB||16GB / 32GB / 64GB|
|Primary camera||8 megapixels||13 megapixels|
|Secondary camera||1.9 megapixels||2 megapixels|
|OS||Android 4.2.2||Android 4.2.2|
It looks like a pretty cynical marketing exercise by Samsung to try to pass off this inferior handset as anything like the Galaxy S4. Unfortunately, Samsung will probably convince many media outlets and customers that it is such a thing..