Yes, the labels are different to some extent, and thus you might get different results with different brain atlases sometimes. The probabilistic brain atlases are definitely superior to the AAL as they are based on 40 (LPBA40) or 30 subjects (n30r83) instead of a single brain only (AAL). There are separate maximum probability maps for the different regions and a single "brain atlas" file with different regions coded by number (look at the included PDF or text files for corresponding brain regions). Concerning "template", you would have to preprocess your data so that it is MNI space at the end, as these brain atlases are in MNI space (similar to the AAL).
People might still prefer the AAL because it has it's own toolbox or because they stick with what they've learnt (AAL was released already in 2002), whereas the brain atlases mentioned above "just" provide the different nifti files.
I'm not into diffusion MRI, but if you're interested in white matter / fibre tracts you might want to try the corresponding files provided with the SPM Anatomy toolbox.
Best,
Helmut
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