You should always expect some level of splashing from a rain chain, with more splashing in heavier rains. However, in our experience there is never enough splashing to cause us any concerns!
The link type chains most closely resemble traditional Japanese chains and tend to spash more than the cup types. However, a dripping link chain in light rain looks great and the column of water that develops in heavier falls is specacular. But as the cup types have open bottoms, they work more like funnels which channel the water into the container or drain below.
If you are concerned about whether rain chains are suitable for your situation please consult a licensed plumber.