Opinions vary on if its better to go with global or cdma/4glte. I recommend global, and here's why:
Some people have stated MMS sends faster when set to global over the other options. Additionally others have said having global set leads to less time that the phone is searching for signals. A person in Texas reported when set to LTE/CDMA his/her phone would search for a signal for up to 2 minutes when switching between towers, but when it was set to Global it took 10-15 seconds in those same areas.
On my old phone (a Samsung Stratosphere) it only had the LTE/CDMA, and CDMA options, and there would be times when my texts (and/or picture messages) didn't go out (staying in pending status), and times when it would say pending and actually have sent. With my new phone (a HTC One m8 set to Global) everything sends right away. I also find places were I encountered low signals, or slow connections with my old phone seem to be connected at 4G LTE, have stronger signal strength, and faster speeds with my new phone. While the phone itself, the texting app (default on the old phone, but Verizon Message on the new), and other things (Android version 2.x vs 4.4.2) may have been factors in the issues I believe the global setting is a big reason why things run so smoothly and quickly now.
My thoughts are the less time your phone spends searching for a connection the less battery it will use, and the faster your connection and speed the sooner you are done doing what you were doing, and the sooner you can sleep your phone (using less battery then when your using it). As a result my suggestion would be to use global.
As you may have noticed I didn't mention the note 3 since I have tested it out personally, but I believe being on the same network (Verizon) and the HTC One m8 and the Note 3 sharing many similarities (Android OS version and apps) the global vs cdma/lte results should be pretty similar.