The Samsung Galaxy S III mini has a long list of connectivity features. Let's start off with the basics - quad-band GSM/GPRS/EDGE and quad-band 3G (AWS is missing though). The 3G connectivity is backed by HSPA (14.4Mbps downlink, 5.76Mbps uplink).
The Wi-Fi support covers a/b/g/n, with both 2.4GHz and 5GHz band compatibility. Wi-Fi Direct and DLNA are part of the package, of course.
There's also Bluetooth 4.0 LE, which incorporates Bluetooth 3.0, but also includes the efficient Low Energy mode.
In some regions the S III mini has NFC connectivity. It lets you share all sorts of media via NFC by simply touching the devices back-to-back. You'd need two S Beam-enabled devices to get this to work - while not many models support it, there are plenty of Galaxy S III's around.
You can share with other NFC devices as well, but the functionality is limited to what is provided by Android Beam - Android's stock NFC tool.
The Samsung Galaxy S III mini has the Jelly Bean version of the Android browser, which has been tweaked by Samsung, but Chrome came pre-installed too, if you prefer it instead.
Anyway, the default browser supports both double tap and pinch zooming along with the two-finger tilt zoom. There are niceties such as multiple tabs, text reflow, find on page and so on. A neat trick is to pinch zoom out beyond the minimum - that opens up the tabs view.
The Web browser comes with Incognito mode, which enables you to surf the web without the browser keeping track of your history or storing cookies. You can also switch to a more minimalist UI, which currently is in a Lab stage. It disables most of the browser's user interface and gives you a quick five-button layout to access the basics.
One advantage over the regular browser over Chrome is plug-in support, more specifically Flash. Of course it doesn't come pre-installed (Flash isn't officially supported on Jelly Bean), but you can grab the APK for ICS (here's the archives page at Adobe that holds all past versions) and it will work.