There are two main categories in the car shipping business with regards to the services available.  There is door-to-door and terminal to terminal.  A terminal is a hub, very similar to that of an airline.  Carriers use these terminals as locations to pull all the vehicles into one central location for a convenience and in some cases, unload/reload their trailer.  This gives the transporters the option to allow smaller trucks to deliver/pickup their cars.  In cities like Los Angeles and New York it is far more convenient for a smaller truck to get around the city because of traffic and size of the carriers.  It is no more or less safe to have your car transported door-to-door or terminal to terminal.  Assuming your carrier is reliable it should not make a huge difference on the overall timeframe either.  Of course, because the car transporter needs to do less work your price will be cheaper for you to use the terminal service, but you then need to get rides to pickup and deliver your vehicle.