iPhone 6 new folders for mp3 files
Take a look here. I use Documents (by Readdle) that works fine and it's free. 

You can get files from your computer, sync with Dropbox, iCloud, other cloud services and any source you can imagine. You can also download files from the Web using built-in browser. Organize the files into folders for your convenience using the brand new file manager. 
You can manage different file formats and also read and modify PDFs. You can also create folders, according to the different contents.

Obviously, you will never have Android performance (system specs are very different) but I think this app can be a good compromise.

You can easily download the app for your iPhone following this link.