I always looked at the H-Shifter with fear in the past. Whenever I tried it before I had serious problems to get the synchronization on my movement right.
Then, just for fun, I tried it with the F1800, and surprisingly I found it very natural and immersive.
At the moment I'm always using it, and after a bit of training I can be as fast as with the paddle or even more. For sure my racing experience is improved, because it's much more realistic and addicting.
It can eventually give you some advantage, since you can shift without releasing the throttle if you want, but, you need to master this movement first.
So you can eventually gain 0.5 sec per lap (so much???) as Michele said because of this, but maybe losing a lot more if you are not used to it.
I personally advice everyone to try to use the H-Shifter just because it's much more fun.
In our team we all tried it, just for fun, and now we can't drive without it!