In both cases, you can't slide the ball across the rubber. They should both grip well.
But a good tacky rubber when new might even be able to pick the ball off the table if you press the paddle on it. Or if you touch it with your finger, the surface will actually feel stickier.
Some general beliefs (your mileage may vary) is that tacky rubbers actually grab the ball better or more. Have higher spin potential. But since they also hang onto the ball more for a fraction of a second compared to grippy, which are not sticky, they're a hair slower than grippy in theory. The ball rebounds or springs off grippy faster. Again I'm generalizing here and rubbers vary between them.
Try them both. See what style suits you better. It's completely a personal preference thing. After trying euro rubbers twice as expensive, I still prefer the Chinese tacky rubbers. But that's just me. The next poster in this thread could easily feel completely the opposite.