I don't know if I'd say it competes with the Droid Maxx. The Note 3 & 4 are going to be similar so I'd say around 5 hours of display time. Is that good enough for your needs?
Samsung Galaxy S5 (Verizon)
I have two spare batteries, and my Note 3 has performed many a 15 to 20 hour non-stop movie playing sessions, with only a 30 second break to swap out the batteries! Everysince I had my Note 3, I have taken full advantage of the removable battery. I keep two fully charge batteries with me at all times. On those storm and snow in outings, the Note 3 is playing full time, swap out the battery with a fresh one, and throw the spent one on a battery charger. With this system, I could go on forever, or until the Note 3 breaks, all with just 30 second battery changes!!
I will be getting two spare batteries and a charger as soon as they come out. I considered SPARE BATTERIES a MUST HAVE!!