Definitely. And we're both often compared to San Francisco, which is a wonderful compliment.
As for rivalries... while we're both very small cities, Halifax is larger by a significant enough percentage that there isn't much competition. We're in different little leagues, ha!
However, St. John's isn't accurately well known in Canada and I find the farther west you go, the more accurate the impression of the city becomes. Conversely, people in the Maritimes have some pretty unusual views about Newfoundland.
In Halifax, for example, I heard far stupider things about my city than in Vancouver. I remember being laughed at when I said St. John's was one of the largest cities in Atlantic Canada. I remember a taxi driver saying, "You must be excited to drive on a divided highway! They don't have those in Newfoundland!"
So that could be a sign of past, historical rivalries, perhaps? But today, there's not much. Many of my relatives live in Halifax and the surrounding area.