Simple analysis of the operation of Free Will in our Lives, without engaging ourselves about Free Will in philosophical terms, would show we are not free.
When we perform an action, choices presented to us are limited.
We do not have access to ALL options.
We act on the basis of choices presented to us at a given point of time.
Hence we have Free Will as well as we are Limited.
The difference between Mantras and the other two Types is that Mantras deliver guaranteed results, if one follows the procedures laid down.
Whereas in the case of Stotra or Parayana,the Divine intervention is left to the pleasure of the God addressed to, in the case of Mantras, the Gods are obliged to grant the requests as they represent the essence of Reality and in fact the Form of Gods themselves.
That is why even A Raskshasa can deliver a Brahmastra by invoking a Mantra.
More to follow on the scientific explanation of Mantras, their validity analysis by Spectroscopy,Cymatics
There have been specific researches conducted on the Mantras, including the Gayatri Mantra and OM.
I am quoting the excerpts of three different researches on OM,relating to OM’s resonance effects on the Brain, on Cerebral Cortex where the Blood supply is improved,Mind calms down, Blood pressure is brought under control.
These experiments were conducted by eminent scientists, not all of them Indians under strict research procedures.