MOSFET vs. relay power efficiency
Your choice depends on a lot of things:


Are you switching AC or DC?
What is your switching voltage? (5/3.3V from a microcontroller? 12V from a battery? You mentioned and Arduino/RPi/Xbee but what exactly is doing the controlling, and is there any other power sources available?)
Switching speed
Thickness of your wire (how much power have you already lost from just copper losses?)


Efficiency is much of a muchness, and while relays might "seem" more efficient because they are a galvanic contact, that is definitely not the case. Just now with a quick google I found a relay with 0.1Ω of resistance rated for 15A (here). This gives a power loss of:

\$ P = I^2 \times R = 15^2 \times 0.1 = 22.5W \$

On the contrary, I also just now found a MOSFET with an on resistance of 0.005Ω (here). This gives a power loss of:

\$ P = I^2 \times R = 15^2 \times 0.005 = 1.125W \$

Yes - you can choose a higher-rated relay and that will have a lower contact resistance, and probably you will find one even more efficienct than the MOSFET. But  that will cost more. Is cost a concern? The list of factors goes on.

Just goes to show you can't assume anything. If you give more details of your project I can help further and edit my answer, but for now it's very open-ended and frankly, depends on a lot of factors you haven't mentioned.