Bladder presses deliver more surface area contact when pressing, making them more efficient and more gentle.
A friend of mine had one. He was not too careful about sorting his grapes and a nail (from one of the grape crates) managed to puncture the bladder.
He used water to inflate the bladder, so in the end, he did not have a spare bladder, had water leaking all over a working press, and still had several hundred pounds of grapes to process.
If you do get a bladder press, make sure you have a spare bladder on hand (just in case).