Can't say that I have tried many of these.
But I did research on Alder Cones before for my shrimp tanks.
Take a look at this info here detailing the rate of release and pH effects using Alder Cones
Alder cones - How alder cones affect pH and color in aquarium water
I've used Cholla wood, although on a large tank, and I didn't notice any tannin tinge to the water at all, but driftwood would release enough tannins to turn the water a light tea color.
So as far as tannins, my sourced Cholla wood didn't release much at all, but the "wood"/cactus itself has been in the tank for over a month and hasn't "dissolved"/broken down much at all (then again these are in a tank with fish who show no interest in it, no shrimps in tank, some snails, but haven't seen them munch on it). And well, drift wood lasts a long time. I have found Mopani to leech a ton more tannins than Malaysian driftwood.
As for medicinal properties, I've heard Cattapa is not as good as Indian Almond Leaves.
Supposedly Banana leaves are fairly good for medicinal purposes.
I've seen Cattapa bark as well, but don't know much about it, but it should last longer and have more tannins.