What's the fastest way to migrate an Oracle database from Unix to Linux?
Is hard to say which method is faster, but I would say from my experience using source backup is faster than import.

It seems the issue you see with the file header when you use the source files comes from the file format of AIX which is big endian, while on Linux is small endian.

The files need to be converted. This can be done using RMAN:

RMAN&gt; convert datafile 'bla' 
    TO PLATFORM="Linux 64-bit for AMD (or your platform)" 
    FROM PLATFORM="AIX-Based Systems (64-bit) - or your platform"

    (note: line breaks added for readability)