I have researched this topic a bit. One site suggested that prodigal is having reformed after being wasteful, while profligate is still engaging in such behavior.
However on studying the origin of the words, I found that this might not be correct. The parable of the prodigal son was the first reference of prodigal (from the resources I came across), and the parable is also referred to as the parable of the profligate father. Seems like prodigal is related to immorality somehow.
And studying the etymology of profligate, it seems to be linked to downfall.
What exactly is the difference between the two?
Profligate has a semantic center of gravity that leans more towards general licentiousness and moral degeneracy, whereas Prodigal is more tightly focused, pertaining specifically to extravagance and wastefulness.
You could validly use profligate as an alternative to prodigal, but there are many times when prodigal would not be appropriate to use in place of profligate.