I just purchased a new 2015 Ford F150. It has the full navigation, ford sync with mytouch. The issue is that it will not access text messaging on my Note 4. My phone pairs through Bluetooth correctly and downloads my phone book but if I try to send a text message through Ford Sync it tells me my phone does not support that option.
I tried using my wifes S6 Edge and it works perfectly.
I would contact Ford about it. When I bought a new Toyota I paired my Droid to it and could use all it's features, but when I bought a new S5 I couldn't do anything except use my phone to supply the Toyota system with internet and then use their provided apps.
That said, you could go through the motions of making sure everything phone and car system is up to date; though both are new so this most likely isn't the case. You could forget the network on both the car and phone, delete the cache and data on your Note, restart and try to pair it again. I'd also browse Google for a relate-able issue.
My understanding is you have 2 different phones; Samsung S6 and a Note 4. It's not uncommon that one phone would work and the other wouldn't. Unless they are made identical on the inside and just look different on the outside, which I don't believe is the case.