Haven't had either, but I will say the Murano has a variant or has the venerable VQ35DE V6 which is one of the best engines of all time. I have had a couple vehicles with that engine, its awesome and reliable beyound reproach.
Now if the Murano has Nissan's CVT run the hell away. They have never gotten the CVT right and I'm a big Nissan fan.
I have driven both and have to say the ride and driveability I like the Edge better.
If you are interested in reliability and mpg rating try
www.truedelta.com. You can see all their data just by answering their questionaire about your current vehicle.