Hey again,
First off, traditional Euro/Japanese rubbers are not even slightly tacky since they don't stick, but they are grippy thanks to their porous sponge and tensioned topsheet.
The main advantage of tacky rubbers, especially the traditional Chinese ones, is the spin potential. They're also great for serves, serve receives and the short game. They have very good control for the most part, and are more predictable (what you do is what you get). Finally, Euro/Japanese rubbers bottom out, meaning that there's a limit to how much speed and spin they can produce, whereas with Chinese rubbers, the more you put in, the more the output (the only limits being your fitness and technique).
An hybrid rubber combines a Euro/Japanese porous-type sponge with a a "tacky" topsheet (usually a lot less tacky than Chinese rubbers). It will be springy like regular rubbers, usually a bit less fast than it's non "tacky" conterparts, but will have better serve and short game potential. It's an in-between type rubber between Euro/Japanese and Chinese rubbers, averaging out the qualities of both but not really reaching the peaks of either.