I've had no issues with the Moto360. I've also used it with an iShower speaker, an LG Bluetooth Stereo, and my car. I did notice that it would disconnect from my car around 5 or 6 feet, but then again, I never tried getting out of my car with the phone in my pocket when I had the Note 3, so I can't compare.
I only have a LG headset for music and stuff and it seems to be the same as my Note 3. I can keep it on my desk at work and walk around the corner to the sink to wash out cups and it keeps playing without a hiccup.