Problem Transferring old text messages and old notes- phone provider related issue?

I am not able to transfer old text messages and old notes from my old at&t iphone 6plus to my new verizon iphone 6plus. I have transferred most information from icloud and transferred manually through icloud, but my texts and notes from my note pad will not transfer. Does this have something to do with phone providers? Should i install my old SIM chip into my new phone? I also just moved to israel and there are no apple stores here so this can be tricky. Please help.