This is essentially my opinion. I find the Stamina Gauge to be completely redundant as far as The Legend of Zelda is concerned; it offers no benefits and it certainly stifles creativity with runs through the game. Through my experience with Skyward Sword, where most puzzles and objectives were little more beyond "get from point A to point B in a straight line with a few angles here and there", the stamina gauge just limited my fun and of course made "strategic" runs even more bothersome.If I'm completely honest, I don't really think I want it back, not because I think it's bad (I don't think that) but because it doesn't really do anything particularly beneficial.
All the Stamina did was limit Link's ability to sprint and climb. Imagine having a Stamina Gauge in Assassin's Creed; the game would be unplayable. Zelda is similar in the way that you're always gonna be moving as fast as you possibly can. This is why there have been so many tricks and even glitches discovered to help you get around faster. So to give us a sprint function but then limit it in such a way just stunted the ability to sprint, as far as I see it. Why give us one thing only to limit it with another?
So from my experience on Skyward Sword, the Stamina Gauge stunted the welcome inclusion of a Sprint and was completely redundant when applied to climbing. So I suppose I have no idea how they would improve it beyond just getting rid of it. It was a nice idea but I think it doesn't really have a place in The Legend of Zelda.
The way I see it, the Stamina Gauge could only be beneficial (and making it beneficial is how I'd improve it) if the Zelda game in question was a turn based RPG of some sort; in a real-time action adventure series it limits the gameplay and creates several issues (read: redundancy) that SHOULD be non-issues. So, there you have it: I'd improve the stamina gauge by making the next game a turn-based RPG.
To improve the dash meter I'd want them not to assign nearly every single movement Link makes to depleting it.
It could also do with a charge mechanic too for stronger attacks or burst running (kind of like pegasus boots)
I really agree with Spirit's notions; should the stamina gauge come back as it did in Skyward Sword, I'd like for it not to be assigned to every single moment Link makes. Why? It becomes tedious, not fun, and really just in the way (as it is, for me). The bit about a charge mechanic would be GREAT! Just think about all the possibilities with charging sword slashes, spin attacks, and maybe even Hidden Skills!
Oh, one last thing. If it DOES come back (and I'm crossing fingers that it doesn't), I'd love for the Roll to be much more efficient than sprinting. Sprinting takes much more energy out of you in the real world than rolling does, and although rolling is technically more dangerous (head injuries, go figure), it's more efficient IRL. Transfer that to the game world, huh?