On average across the year, yes, Nova Scotia is hotter than New Brunswick . Nova Scotia has an average temperature of 7°C/45°F and New Brunswick has an average temperature of 6°C/43°F.
Nova Scotia's hottest month is July, with an average maximum temperature of 24°C/75°F, which is not hotter than New Brunswick's hottest month (also July, with an average maximum temperature of 25°C/77°F).
On average across the year, no, Nova Scotia is not colder than New Brunswick . Nova Scotia has an average minimum temperature of 3°C/37°F and New Brunswick has an average minimum temperature of 1°C/34°F.
Nova Scotia's coldest month is February, with an average minimum temperature of -9°C/16°F, which is not colder than New Brunswick's coldest month (January, with an average minimum temperature of -13°C/9°F).
On average across the year, yes, Nova Scotia has more rain than New Brunswick. Nova Scotia has an average annual rainfall of 1040mm and New Brunswick has an average annual rainfall of 973mm.
Nova Scotia's wettest month is December, with an average monthly rainfall of 112mm, which is wetter than New Brunswick's wettest month (also December, with an average monthly rainfall of 105mm).