Why should I choose a bank over a broker for my investments?

There are probably good banks as there are probably good brokers. The problem is finding one. Your best bet is to interview prospective candidates with a set of very pointed questions.

Such as how many years of experience do you have? How long have you been in your current position? What are your fee schedules? What serviced do you offer?

Frankly, I am very happy with Fidelity and TD Ameritrade. Both offer good service and a very wide variety of investment options with excellent fees.

Depends on which is better and who charges more.

Go to a bank for a loan. Find a broker for your investments. You need to decide what level of service you need. Deep discount, discount, full-service, planner ... Do you want to pay fees or a commission? A bank shouldn't even enter into the picture. I know people use them but 90% of the time they are not getting the advice and knowledge that they are paying for.

You never should. Never.

Many banks have a brokerage divisions/affiliate (becoming more common these days). Also, many brokerage firms are adding bank services.

The lines are quite blury these days. For instance, Bank of America brokerage affiliate is Banc of America Investment Services Inc. Washington Mutual calls theirs WM Financial Services (WMFS) and it is an affiliate of Washington Mutual, Inc. and its banking subsidiaries.

You should work with someone that you feel comfortable with, regardless of their affiliation.