I've played with triangle hard tips for about 8 years (always on a regular shaft), and they've allowed me to do everything I've ever asked of my cue. I've never had one mushroom on me, but I also don't break with them, and I'd describe my game as more of a finesse game than a power game.
I've never had a bad one, so frankly, I'm surprised to hear that it seems to have been a problem for some folks. They're rarely squared off on the bottom, but that's easy to fix with some sandpaper and it doesn't sound like the kind of "bad" that people are talking about.
I used to shape my tip a lot before I realized that it was sort of a fruitless endeavor, and I went through quite a few tips because of it. I used to put them on myself to save money, but I guess I was lucky and got all good ones?
I've messed around a little bit with layered tips, but I don't have enough experience to really make a fair comparison. But, if I had to guess I'd say that they were rather hard by comparison when they first came out, but now they're closer to medium hard. They're certainly harder than LePros if you're familiar with those.
Hope that helps. Nice looking cues by the way.