I have not run across a good Le Pro or Triangle tip in a while, the last few I used basically were shredded wheat, structure was not good. The Outsville KiTech tips were good, I used two of those and both were very consistent in hardness rating and stayed shaped.
While a single piece tip is defiantly "classic", I don't think it has any advantages at all over a layered tip. When me and a friend of mine did some shaft and tip tests years ago we had one setup that were two of the same shaft, but one had a layered tip (don't remember the brand), the layered tip got more spin on the ball over 10 different attempts. It was a pair of LD shafts made by Mike Webb, he had two different tips on them, we used a low right spin shot from near a rail with an angle to see how far down the other rail we could get the cueball, the most spin we got was with an LD shaft with a layered tip, the least amount of action we got with a normal shaft with a single layer tip. I posted this several times before, it was a pretty interesting result, with both of us shooting each shaft/tip combination 5 times, the position of the cueball was very consistent based on the equipment used, the LD shaft and layered tip got over a diamond lower on the rail.