These questions will be difficult to answer unless you look at school rankings and take from that what you will, or if you ask someone who has been to both schools. I'll answer what I can from my perspective at Brock.
1.Quality of staff
Varies by the department. I don't know what their staff is like for the MBA program, but I've heard that the business department has good instructors.
2.Cost of living in both the cities
Rent is expensive if you live on-campus, but off-campus you can find places between CAD$300-600, depends how nice and where you want to live. Around $450 is common, and most places include utilities like water + electricity + internet in the rent.
Groceries are affordable if you buy stuff on sale. There's lots of grocery stores around.
Getting around is easy by bus. You will get a bus pass included with your tuition that lets you ride the bus for "free" during the fall and winter semesters.
3.Quality of the program
I don't know first-hand, but it's a popular program.
4.Getting employed once done with the course which is highly important.
St. Catharines is in Ontario, and there are a lot more employment opportunities here than in New Brunswick. But you can always relocate after you finish studying, so not a big deal.
5.Campus life
Any specific questions about campus life? There's lots of student groups and activities going on usually, so it's easy to get involved if you want to. The school has some nice facilities like a gym and track, but that stuff is pretty standard anywhere.
6.Carrier Services.
As in services for mailing stuff? There's the Canada Post Office, and there's some private businesses like Fedex, Purolator, etc. You can mail stuff from Brock as well.
7.Internship facilities.
I don't know if the MBA program has a co-op program. But co-op is popular at Brock. You should find a paid job easily if you're smart enough to get into co-op.