Before you read, I want to make a disclaimer. All of my opinions come from experience. There is no exact science here. It comes from a personal experience with H3, but there is no guarantee that they represent the real quality of H3 (including commercial, Provincial and National).
There are some disadvantages of H3 when it is compared to Tenergy. But I would rather say that they are different kind of rubber with their unique pros and cons.
But for those who want to stop using H3 before really trying to get into its real power, let me share some reasons why I continue to use H3 (about 5 years to date):
1. H3 gives me a very spiny service, chop, loop and top spin. I thus gives more edge in the play.
2. It is good for service return. However how strong the spin of the service, it is considerably easy to control the ball, because it is not bouncy. (mistakenly, some people for this reason use it in backhand i.e. they have difficulty returning a spiny service at the backhand side. In this case, it is better to learn backhand receive and flick rather than using H3)
3. The loop from H3 is very spiny, low arc and considerably short. True, H3 is not great for smash. But the opponent will generally have difficulty to block or control the ball. The loop and top spin from Tenergy and similar rubbers are easier to predict, both its direction and its amount of spin, H3 is more difficult.
4. The combination. Because I use Japan or German Rubber at my BH, I find the combination is quite effective. With spiny loop and top spin from FH, then a fast and forward punch and top spin from BH. The success rate of the attack is generally high.
5. With H3 I find it is easier to play close and middle to the table. When I tried to replace my FH with tenergy, for example, it forces me to get into middle distance most of the time. If you like to stay close to the table, you might want to consider H3.
6. It has also considerably more edge in touch, placement and drive. The sticky surface somehow gives some unexpected spin to a ball that otherwise a no-spin stroke.
Again, this is just a personal taste and experience. It might not suit everyone.
In the past I always use H3 with speed glue. But with the ban, I tried Neo versions of H3 and Skyline-3. Without speed glue, H3-National version is the worse. It is hard, slow and heavy. The blue sponge is even harder to use. But with speed glue they are really monster. Also, in my opinion H3-P with speed glue is the best for a club player, although it is easily wear-off, and in some cases created some bubbles in the top sheet. With the Neo versions (I only tried the commercial/8 edges and provincial/6 edges), it lasts longer and has a better consistency.
If you want to try H3, look for a softer sponge (this is a major difference with Japanese sponge which only have two version: normal and fx). The best to start is the sponge with hardness 38-39. But seasoned users will like to use sponge with hardness between 42-44.
Finally, I would say with Japan and German sponges, the ball last longer. Because the rubber grab the ball into the soft material. With H3, the ball will slightly deformed in the hitting. So chance is, the ball will have a shorter life