I'm not 100% sure what I think about Mantle yet.
I see obvious reasons for AMD to push it, they are (GCN) in the consoles, they are simply bringing/using optimizations across the PC/Xbox/PS.
The obvious drawback is vendor specific optimizations.
I don't think Physx will succeed as long as it's only added by paying developers to include it. Physx for example would have a lot more potential if they both built on it and it was included everywhere, then it could be more than some cloth awkwardly flapping in the breeze, or liquid that only breaks in blobs.
I guess Mantle will be similar in a way, however the consoles ensure that ports will be coming for years, so they have a guaranteed ~7(?) years with support. In that way I'd say Mantle has a real chance to be in the market for a long time. Yeah Physx and Mantle are two completely different things, however at this point they are exclusive which is the similarity I refer to.
The thing is that if only one vendor is optimized, half of the market loses something. Ideally (imo) NV will implement the API themselves and gamers are back on level ground.
On the other hand, NV and the insistent followers keep pushing "exclusive" features, regardless of how gimmicky they are. NV is the leader of trying to exclude the other imo, so in a way they get a dose of their own medicine. They are trying to do gsync and certain people are thrilled about it, yet at the same time they complain about mantle. This goalpost shifting (on both sides) is annoying and reeks of marketing imo (it may be the supporting ones own purchase?). I don't want to be 'forced' to buy a certain manufacturers card (for whatever reason) since you know what that will do to prices.
That said, the way the gaming companies are starting to portray it sure sounds appealing. I'm guess it will be a significant improvement over current Dx versions of the same game. If nothing else it should be easier to port games over or offer benefits ($/time/other?) to the developers for them to come out and speak highly of it?