Is there any advantage of one of these types of switches over the other?
The one on the left is old, quite old, early 1960's to early 1970's I'd say. The one on the right is the new replacement for that old style breaker. 

The replacement for the one on the left is a non-CTL BR1515. See the question/answer here: http://www.amazon.com/BR1515-Circuit-Breaker-Without-Rejection/forum/-/-/1?_encoding=UTF8&amp;asin=B002YF912M