The main reason why 64-bit processors are needed is to utilize hardware configurations with more than 4 GB of RAM. To make this possible, the operating system also has to support the architecture, and apps have to be properly designed as well.
This is the case with PCs which top the mentioned memory capacity and have the right software for it, but when it comes to mobile devices the advantages are mostly limited to bragging rights at the moment, with a few exceptions (like Microsoft's Surface Pro 2 -- it runs the 64-bit Windows 8.1 Pro and can be had with 8 GB of RAM).
Apple's iPhone 5s is the best example of why having a 64-bit processor offers no real benefits (other than allowing developers to adjust to the change): iOS 7 and the apps may support the architecture, but the smartphone ships with just 1 GB of RAM. This means that at no point is 64-bit needed, because the memory capacity does not warrant it. Former Qualcomm chief marketing officer Anand Chandrasekher was among the first to point this out, but here we are today with the US company also revealing its own 64-bit processor, dubbed Snapdragon 410.