Coinbase actually aren't like a normal exchange in that they don't have different prices for buying and selling. They seem to cover the difference themselves somehow, and they have very high fees (1.49% as they show
here).
Bitstamp's fees get progressively less the more you trade and are detailed
here.
Coinbase's website and their services have been experiencing some downtime recently, so personally I would feel better on Bitstamp.
This is a big misunderstanding.
Coinbase isn't an exchange, but does have an exchange. When you log into gdax.com with the credentials of Coinbase, you have a very good exchange.
Makerfee 0%, takerfee 0.25% (or lower when you have high volumes). Transferring money between Coinbase and GDAX is free of charge.