Powerline is not much more secure than Wi-Fi. It may travel quite far outside the house.
If you use strong encryption and a decent passcode, Wi-Fi is perfectly secure, unless you are a high-end spy. - In which case, I'm sure your handlers will have provided you with adequate solutions.
Hans
The physical advantages of powerline over a CAT5 type wire is:
a: You don't need to string wires around your home or have to deal with getting the wires inside the walls.
b: It is portable so that you can move the device easily as long as you have an outlet available.
Security wise I can think of these advantages:
a: It is encrypted (WiFi can be too of course so it's not so much an advantage over WiFi as it is an equal but it does need to be mentioned).
b: It is much less likely to be hacked into simply because you need to have a compatible device on the same circuit (in this case circuit means sharing the same transformer on the utility pole). No drive by or war driving.
c: The software that you use to set it up will tell you if any other device is present and connected and you can check it at any time. You can do this with wireless too of course but it's not a one click and check type deal.
d: Interference is a non-issue. No more "Dead spots" where your WiFi doesn't work well.
The disadvantages are:
a: It's a hub type system not a switch or router so adding powerline adapters will slow them all down. As long as you are using a higher speed adapter this shouldn't be an issue as long as you don't go crazy with it. 4 max would be my guess, that should keep it at or near 802.11.g speeds.
b: Expense. While they have come down in price a good one will run you about $125 a pair out the door.
c: There are some electrical situations where they won't work. Improper wiring (by that I mean wiring not installed up to code may not work, knob and tubing will still work though so age isn't an issue), most power strips will not work either (it has to do with the surge protection).
Overall I think that it falls somewhere in between a CAT5 hard wired setup and a wifi setup. Not for everyone but a good option to consider where mobility isn't an issue or is not a viable option and you are considering running cable.