A secondary IP address is usually assigned to a physical interface on the router so if the interface goes down then the IP is no longer reachable.

They are used for a number of things although I have to say I have never had to use one. An example of where you might use one is if you were migrating devices from one IP subnet to another and you temporarily used a secondary IP address for the new subnet on the L3 interface.

I'm sure others could point out other uses.

A loopback interface is a logical interface on the router and is not tied to any physical interface. This mean unless the entire router goes down the loopback interface will always be up.

Because of this they are used quite frequently in terms of router ids, multicast RP addresses, management interfaces, router peerings etc. The advantage being that if a router has multiple interfaces and redundant paths etc. if one of the physical interfaces goes down the loopback IP is still reachable.

They are also very useful in lab scenarios where you can configure multiple loopbacks on a router and advertise them into a routing protocol etc. which means you don't need a router with a lot of physical interfaces.

I would say from my experience you will come across loopbacks far more than secondary addressing.

Jon