I prefer "chisel point" to "tanto point" because Japanese tantos had other tip designs and not everything with a chisel point is a tanto(technically). So now we have "Chisel grind" which, to me, means the blade's main grind is one sided. "Chisel edge" for an edge ground on one side only (but everyone calls it a chisel grind anyway) and now the "chisel point" just to make things confusing.
My beef with Tanto/chisel points is how some manf's build them. If it has the curve, it is good at BOTH slashing and stabbing. But I see so many knives with crazy ideas like "drop-point tantos" where the tip is centered but the upper half is a swedge. The POINT (no pun) of a tanto tip is to have a full profile SHARP edge as you stab. Having half the stabbing profile blunt is worst then useless (read: counterproductive). And if the tip is ground thin like a cheap dagger's is, then the chisel design losses its main advantage of strength. If it is thin enough at the tip, then a curved point actually has more strength due to more metal reinforcement in the vertical plane.
If the tip is not level to the spine, or preferably above it, I'd say leave it alone. Add a slight curve to the blade and one has a truly useful weapon and tool. This was the great thing about CS's original tantos. But even they, who had it right in the FIRST place let the idea become perverted. The chisel point on their Recon 1 folders is no more than a faceted spear point.
So to close, chisel tips are good if you find one that is built right. Think before you buy and avoid the nonsense like a long, thin chisel tip with the tooth (second edge) a third of the way down from the tip.
Man, even trying to end this on a good note, I can't avoid thinking of all the bad designs out there.