As best as I can deduce from my research, this is the pedantic difference:
Parlance derives from the French "parler", meaning "to speak", whereas vernacular derives from the Latin for "domestic, native", further derived from the Etruscan for "home-born slave, native". Parlance is defined as "a manner of speaking that is natural to native speakers of the language", and vernacular is "the standard native or everyday language of a country or locale". Therefore, parlance is the language of the person, notwithstanding the location of that person, and vernacular is the language of the region notwithstanding the person. Therefore, parlance would be a purer form of the original language, but may be displaced, whereas, vernacular will become bastardized over time due to the influx of new persons to a new area who change the language. This coincides with the etymologies since parlance just means to speak, but vernacular has that element of displaced household slaves who have had to adopt a new language, but may have added a few things from their former home. Parlance has a connotation of something a little more formal. You will hear "in the common parlance" as a way of jokingly reducing the level of "parlance", but never "in the common vernacular", since vernacular is already impliedly less formal. Also, vernacular encompasses swearing, again consistent with the idea of low brow slaves just talking, but never with parlance. They are, unfortunately, listed as cross-referenced synonyms for each other, but this is obviously wrong. So, in casual conversation, you would say, in the parlance of a language you knew as a native speaker no matter where you were, but you would talk about the vernacular of a region even if you haven't lived there that long and even if you don't speak the regional idioms. That leaves my sentence usages as:
French parlance uses the "r" to distinguish native from non-native speakers, and more particularly Parisians from tourists.
The only vernacular of Boston that I picked up was the exceptional use of "wicked".