The current trend in smartphones is to go big, with many new high-end models sporting 4.7-inch to 5.5-inch displays. That's fine if you are data-centric and have big hands and pockets. However, there are still many people who want a smaller phone.
Samsung officially announced the Galaxy S4 Mini and it will be interesting to see if this smaller brother enjoys the S4's level of success.
I can understand the desire for a smaller display device. I remember a time when people thought the limit for smartphones was going to be 4.3 inches. I am satisfied with my 4.7-inch HTC One and 4.5-inch Lumia 920, but the 5.5-inch Note II is definitely not that convenient to carry around for communications and doesn't go with me everywhere as the smaller devices do.
With the popularity and rise in 7- to 8-inch tablets, we may soon see a trend of people going back to these smaller display devices paired with small tablets. There are rumors of an HTC One Mini and a device with the HTC One build quality — and a 4-inch display could be a very attractive offering.
The Galaxy S4 Mini is not an S4 and has many reduced specifications, including the display quality, camera resolution, battery size, internal storage, and processor speed.
The Galaxy S4 Mini has very limited internal storage (5GB available); since Android doesn't let you install applications to the microSD card, you will be limited by how many applications you can have on the device. The S4 Mini also has a dual-core processor and — given that Android performance is related to processor speed — it is unlikely that you will see the kind of responsiveness you can find on optimized Windows Phone devices.
People may be willing to accept some reduction in performance with their desired smaller display, but I wonder where that lower limit is. I wrote about low-cost Lumia smartphones a couple days ago and how they offer more to the consumer than older generation iPhones and low-cost Android devices. The display of the Lumia 521 is 4 inches and the 82x series on carriers is 4.3 inches. If you want a smaller display device, I recommend you look at one of these Lumia devices.