On average across the year, no, Nova Scotia is not hotter than British Columbia . Nova Scotia has an average temperature of 7°C/45°F and British Columbia has an average temperature of 9°C/48°F.
Nova Scotia's hottest month is July, with an average maximum temperature of 24°C/75°F, which is not hotter than British Columbia's hottest month (also July, with an average maximum temperature of 25°C/77°F).
On average across the year, yes, Nova Scotia is colder than British Columbia . Nova Scotia has an average minimum temperature of 3°C/37°F and British Columbia has an average minimum temperature of 5°C/41°F.
Nova Scotia's coldest month is February, with an average minimum temperature of -9°C/16°F, which is colder than British Columbia's coldest month (also February, with an average minimum temperature of -2°C/28°F).
On average across the year, no, Nova Scotia has less rain than British Columbia. Nova Scotia has an average annual rainfall of 1040mm and British Columbia has an average annual rainfall of 1054mm.
Nova Scotia's wettest month is December, with an average monthly rainfall of 112mm, which is drier than British Columbia's wettest month (November, with an average monthly rainfall of 168mm).