Schroeder put it quite properly, and this single sentence really can (nearly on its own) answer your question.
The question becomes, "who are you protecting the data from?"
I'd like to expand upon that just a bit, though.
If your only concern is to protect the data from casual eavesdroppers (e.g.: that creepy guy next to you in the coffee shop), then machine-to-machine connection security technologies like SSL are typically sufficient. Presuming the protection mechanism itself isn't weak in some way, you have generally little to fear from people snooping on your traffic.
However, if you are concerned with protecting your data from government agencies, malicious insiders at your ISP, malicious insiders at the app host, your employer's monitoring systems, or other advanced attackers with man-in-the-middle positioning, then end-to-end solutions like PGP are the way to go.
SSL will generally protect the connection between you and the app host. However, if the SSL connection is compromised (i.e.: your company uses an SSL proxy to monitor all traffic on their network as if it was cleartext) then your data is vulnerable. Also, SSL does not protect data at rest in the app host's servers where malicious insiders may be able to exploit it.
PGP protects the data along the entire path, from its origin to its final destination, and protects the data at rest. The only way to compromise the data then is to compromise one of the endpoint machines, obtain a copy of an authorized private key, or find a weakness in the encryption algorithms used. Generally, this will protect you from malicious insiders and man-in-the-middle attacks. However, you must still be vigilant against malware and malicious actors with physical access to either endpoint.
On that last point, it's good to remember a few of the Ten Immutable Laws Of Security:
Law #1: If a bad guy can persuade you to run his program on your computer, it's not solely your computer anymore.
Law #3: If a bad guy has unrestricted physical access to your computer, it's not your computer anymore.
Law #10: Technology is not a panacea.
However, if you're really afraid of those government agencies or other such "big bad guys", you should probably keep this in mind.