I voted for Vancian Magic, which was the least distasteful of the poll options, but still in the negatives. This poll begs for an "other, explain" option.
We playtested spell points at multiple level points, and it consistantly led to novas of high level abilities and then players unhappy with average length adventuring days. Even when the players are like "oh, that wasn't fun last time, I'm not going to do that again." So in my experience a spell point system is worse then a spell slot system in 5e with the context of how fast the other classes like rogue can "put out".
Point based but not level based seems all the problems of that, but removing the barrier of getting access to some challenge-negating abilities (like flight) at too early of a level. It's worse than spell points which is worse than Vancian which isn't particularly great in the first place.
Yada yad, recovery per hour. NO. The absolute last thing 5e needs is yet another different recovery mechanism besides long and short rests. There's already huge amounts of problems trying to balance short rest classes with long rest classes and both with at-will primary classes. Introducing another into the mix for 5e is a no-go.
Exhaustion based: Much like HD based, using resources that will put the character on a very different length adventuring day than the others makes no sense.
Specialize and 1st and they grow but no more choices. Well, there's tantalizing little detail there to be wrong in terms of resource recovery. But considering how players complain about limited spells known, having all of your options set at 1st level seems to be a bad idea. I will give the benefit of the doubt that the "and they grow" would still including things like no flight until 5th and the other limitations on certain abilities by level, otherwise this falls with the problem of getting access to some challenge-ending abilities too early. But in the end, it was just too vague and too limiting to get a vote. This might be a contender with more detail.
But that's a vote for Vancian style out of the poll options, chosen because it is the only viable one. Frankly, that's probably the most boring way to do it. For "psionics aren't magic" people, treating it just like magic mechanically will be a thorn in their sides. It does have "we don't have to design and balance anything new" going for it, but for something this big I would want a different feel. And there's plenty of them that would fit into the context of 5e.
I can say that whatever we get, I want multiple classes and subclasses, including half-psions and 1/3 psions. And for them to work out from a multiclassing point of view much around the same power level of the current "slots add but spells known don't" of casters where.
