As I understand, it’s probably like the difference bettween southern US speak or newfie speak and real english; if spoken carefully, Quebecois is the same as real French. Spoken quickly and with malice aforethought, it can be very different. If they mix Franglais, it gets worse. Acadian French from New Brunswick is supposed to be even more unintelligible.
My stepmother said the rural version sounded like medieval French; watching Mon Oncle Antoine, she said “the fellow just told the other guy ‘thou drunken fool’!”
I suppose a better comparison is between listening to two locals prattle quickly in whatever dialect vs. talking like the announcer on TV. Nobody has a problem understanding the BBC but when I watched Billy Elliot movie, for example, I had to turn on the subtitles even though my parents are from Yorkshire. Subtitled Quebec “slice of life” movies probably were the equivalent of us watching a movie in Yorkshire or Cockney. (Lock, Stock and Two Smoking Barrels).
The former prime minister of Canada and well known brown-envelope-filled-with-cash collector Brian Mulroney used to use local dialect to ingratiate himself with Quebec voters. I only took high school French, but his accent grated even on me. For example, the final vowel is often silent in real French, but in Quebec dialect he would often pronounce the final ‘s’ with a hiss; i.e. Metis pronounced ‘meh-tiss’ rather than ‘may-tee’. I guess he came acrss as a regular Joe, while his opponents sounded like the French equivalent of high-falutin’ Oxford types speaking Parisian French.