I have a Samsung Galaxy S4 that I bought via Telecom in May. I took it to Canada and the LTE on Bell Canada (I have a Bell SIM) worked great. It now works just great here in Auckland, too.
I will soon be receiving a Nexus 5 for Xmas.....a complete surprise, honest....and it does LTE, too. I do not expect any problems.
But in the Android Forum, one poster suggested that LTE phones from the Google Play Store (devices branch) would not work in NZ.
Is this person incorrect? Are there grey areas? Or will LTE 'just work'™ ?