Full towers have undergone a fall in popularity due to the space they take up. However a comeback is seen as more and more people get interested in watercooling technology and its benefits. After all a watercooling system in a bigger case is much easier to fit than in a smaller one. Also an increased interest in case modding benefits the full towers popularity.
A big tower gives you all the space you need for the different components. You can easily fit several hard drives, use SLI and Crossfire setup with easy accessibility. Easy accessibility helps a great deal during the installation process, so if you are new to modding/building then I recommend you to choose a full tower computer case.
Component temperature is another big issue and especially a concern by overclockers. In general CPU temperature usually significantly drops when going from midi towers to big towers. More fans and better airflow comes with a bigger case. Many choose to buy separate fans and/or add other fans for better cooling. A separate CPU fan is recommended by many, and are usually more quiet than the mini-fans that comes along with Intel and AMD processors. Its especially important to change the CPU fans if CPU overclocking is intended.
Water cooling system for the CPU is another route, and many prefer it because of its better temperature handling. Water cooling is also more silent than fans. Today many companies build water cooling sets that can easily fit in a tower computer case. Still some prefer to make their own systems.
Towers today look much more stylish than before. You can pick up full towers especially meant for gamers in mind. They usually come in bright neon light colours and most models have 3-4 fans already installed. Screwless drive bays are common today and makes sliding in PCI-cards easy. Its usually done with a click.
Keep in mind though that several full tower computer cases can reach up to two feet tall and easily weigh around 30 lbs/15 kg. Many cases are built in aluminum, but more and more common is steel. Steel makes it more sturdy, but adds to the weight.
Some towers come with fan control. Personally I find it unnecessarily as you can get free software that does the same trick, and gives you more data feedback and control. An important feature are fan filters. Some towers have them while with others you must buy them separately and install it yourself. Good filters should add no increase in case temperature and keep the computer nice and clean.
In summary full towers benefits you with more space, easier accessibility, better cooling options, and a stylish design.