I wouldn't trust the seatpost mount.; it seems like it could rotate around the seatpost.

I've used the Tubus mounts, and they're very good.
I like the 2-bolt design; one bolt holds the clamp on the stay and the other bolt holds your rack mount.
They come in several sizes, so measure your seat stays and order the correct size.

To be clear, I'd trust the Tubus mounts for the upper mount, but not the lower mount. If your new bike doesn't have any eyelets down by the axle, then you should use a rack that connects to the axle.