Kapil Wattamwar
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Ahir Bhairav,
Love the pen name. Before I address your question, let me me make a disclaimer that you won't find much information out there about these two raagas as they are inventions of Pt Ravi Shankar, and that the following is just my own take.
Charukauns, as the name implies, is where Malkauns meets Charukeshi. Though I haven't seen the aarohana avarohana notated anywhere, it seems to me that it follows Malkauns while ascending, i.e. S G m d n, with the exception of G which is komal in Malkauns but shuddh in Charukauns. Descending, it hits all the swaras, i.e. S n d P m G R. Thus its jati is audhav/sampurna.
Interestingly, the tanpura is tuned to Sa/Ma in Charukauns; if you were to slide the scale such as to make Ma the new Sa, and Sa the new Pa, you effectively have Patdeep.
Parameshwari, also a brilliant creation of Pt Ravi Shankar, is sampurna/sampurna, S r g m D n S' - S' n D m g r S. It's quite different from Charukauns, but they have in common their omission of/lack of emphasis on Pa. The tanpura would be tuned to Sa/Ma in both raagas.
The reason that Parameshwari sounds like Charukeshi is for the same reason that Charukauns can resemble Patdeep; that is, you rename Sa/Ma of Parameshwari to Pa/Sa respectively, you basically have Charukeshi! Charukeshi is sampurna so it would include its rishabh (originally omitted as Parameshwari's pancham).
Thus both raagas have something in common with Charukeshi (S R G m P d n S' - S' n d P m G R S) which might be why you are likening them to each other. Charukauns is Charukeshi without R and P while ascending. Parameshwari is a shifted Charukeshi that excludes P (Charukeshi's R).
Welcome,
Charu Keshi