According to specs, the largest card the phone will handle is 64GB. There is a way, with a piece of hardware (that barely can be squeezed into the phone) to run a larger card than the phone is designed for. Will a 128GB card work in a note 3 without a hardware mod? We'll all find out as soon as someone tries it.
Is the card fast enough for 4k recording, as done in the Note 3? Yes, and then some. 64GB Extremes loaf when recording 4k video. A 128GB Extreme should be at least as fast. (The announced speeds are chip speeds, not the speed you get as seen by the phone. Run A1 SD Bench on your card, whatever it is, and see how it compares to the specs for that card.)