NEXUS 6 looses connection to provider (phone not wireless)

[tsiebold]

I own a NEXUS 6 since December 23rd.
After about 2-3 days my telefone started to misbehave.
It told me that it could not connect to my telefone network (provider).
Even if I selected the provider from the list shown it did not connect.
Sometimes a reboot helped.
But after connecting to my provider the phone lost connection throughout the day day several times, even
being in the open.
The provider has now replaced the SIM card, but the problems does persist.
It is of note that my other SIM cards do not show this behaviour, and, that my SIM card with this behaviour, works fine in my other phone (OPO). Only my NOKIA Lumia 1520 is sometimes showing the same behaviour (e.g. loosing connectivity).

Other issue:
Using the ORANGE SIM card in my NEXUS only gives me a datarate <LTE. Using the same SIM in my OPO gives me LTE rate.

The SIM card is from ORANGE a Swiss provider. I have opened a case with them.

What could be wrong here? Any ideas?
Any help is appreciated.

Thanks a lot.

Thomas