Is this a question about mathematics?

Numeral Systems?

In essence I am asking what is the advantages of our current counting system(base 10), Compared to base 20.

The choice of symbols is separate to the choice of base. The symbols which you call Arabic numerals in the question aren't the 10 symbols used in Arabic. Computer programmers tend to use 0123456789abcdef for hexadecimal. But it seems to me that the choice of symbols is a question of communication as opposed to mathematics (Peano's axioms are the same whatever symbols you use), and questions about advantages of different bases are likely to attract answers based on psychology, linguistics, and other fields rather than mathematics.

Arguably, this numeral system is better thought of as a mixed radix system alternating between bases 5 and 4 than as a simple base-20 system. There's a valid mathematical (or maybe mathematics-educational?) question about the pros and cons of mixed radix systems versus common radix systems (I think it's pretty much all cons, but still).