Hi anakara and welcome!
We don't generally recommend cameras around here. Both Gail and I own the S2, but the choice of a camera is very personnal, so I wouldn't feel confortable telling you which one to choose.
These two cameras are globally very similar. I don't think you will see much differences in the image output in any given situation. So what should guide you is the features, design, and handling. For instance, the H1 has a larger LCD screen, while the S2's screen swivels. Which do you prefer? The H1 has a nice dial in front of the shutter release for quick settings changes, but the S2 has more external controls (thus more buttons, which I like but you might not). The S2's batteries last longer, but the H1 only needs two batteries instead of four.
You see that the differences are minimal, and really a matter of opinion. I'd advise you to go to
www.dpreview.com and look at the reviews of both cameras. You usually find good advice there.
www.steves-digicams.com also offer a great walkthrough of each cameras, telling you how to use its features, the menues, etc. It really gives you a feel of how the camera is used in everyday life, and you can see if you like it. Finally, go to a store and handle each camera, that's the ultimate test. A fantastic camera that you don't like using won't, in fact, be used a lot.
I hope this helped you structure your research. Good luck!