In order to make as many as possible persons are able to transfer their files from one iPhone to another iPhone, there will be 3 ways listed below, which all are my personal experiences.
Method One, Use iCloud to Transfer Files from iPhone to iPhone (The Easiest Way)
iCloud is just the cloud service from Apple, which allow people to upload their files from iOS devices to iCloud, then people can get the files from iCloud on their any iOS devices and computer with the same Apple ID. So with iCloud, which will make the way of transferring your files from iPhone to another iPhone become easy.
In this way, which need you to set up iCloud on both your iPhones (like iPhone 3GS and iPhone 4S), then you'll find you can download the iPhone files from iCloud to another iPhone easily after you push the files from one iPhone to iCloud.
And this way is suitable for people to transfer purchased music, videos, TV shows, ebooks and movies, and also the calender, contacts from iPhone to another iPhone under the same iTunes account.
And with this way , you need to know How to Set Up iCloud on iPhone.
Method Two, Use iTransfer to Transfer Files from iPhone to iPhone (The Best Way)
iTransfer is the known assistant of iTunes, with iTranser, which can allow you to transfer music, photos, videos and ebooks from one iPhone to another iPhone, no matter purchased items or unpurchased items, but calender and contacts.
In this way, which need you to install iTransfer on your computer (Only works on Windows computer so far), iTransfer will remind you to install the latest iTunes on your computer in the installing process. And then you can plug both iPhones to iTransfer, find them from iTransfer bar from the left (similar to iTunes bar), click on one iPhone which contains the files you want to transfer and find the files to right click on the files to choose "Transfer to (another) iPhone", then the files can be transferred from one iPhone to another iPhone soon.
And this way is suitable for those who want to transfer unpurchased songs, videos ,photos and ebooks between two iPhones under different iTunes account, and also the purchased songs, videos,photos and ebooks under the same iTunes account.
And with this way, you need to install iTransfer on your computer (Note:iTransfer can only works on Windows computer)
Method Three, Use iTunes to Transfer Files from iPhone to iPhone (The Common Way)
iTunes is the official tool from Apple for people to sync files from computer to iPhone, which also is a great tool for people to transfer files from iPhone to another iPhone.
In this way, we need to transfer files from one iPhone to iTunes first, the method is like below.
Step1, Go to devices preferences on iTunes;
Step2, Check the option "Prevent iPods, iPhones, and iPads from syncing automatically";
Step3, Connect the iPhone which contains the files you want to transfer, go to 'File' menu on iTunes to choose "Transfer Purchases from iPhone".
Then the purchased things can be transferred to iTunes soon, then connect your another iPhone to iTunes , then to sync it with iTunes, then the files from the previous iPhone will be transferred to this iPhone soon.
And in this way, as the same as iCloud, you can only transfer purchased music, videos ,photos and ebooks, and also the calender and contacts between two iPhones under the same iTunes account.
So, these are just the 3 methods to transfer files from iPhone to another iPhone with my experiences, hopes it can help those who are not know how to transfer files between multiple iPhones.
