For work I've recently been to London, Paris, and Berlin. Each city has a municipal bikeshare system.
The London and Paris systems are similar: many rental racks throughout the city, where you grab a bike, and return it to any rack. In practice the Paris system is more user friendly IMO, because it seems like there are many more racks (one every couple of blocks sometimes), each rack has a map of other racks (handy when you come across an empty rack, which only happened to me once), and the checkout system is simpler. The Paris bikes are more solid, but on the other hand the Paris system is much more heavily used, so the bikes get more abuse. Paris also gives you credit for dropping off a bike at the top of a hill, which is cool. (London and Berlin don't have hills.) The Paris system feels like it was designed for usability, whereas the London system feels like it was designed as a marketing plan.
The Berlin system is completely different: you can pick up or drop off bikes anywhere. A smartphone app tells you where all the nearby bikes are. When you find a bike, the app gives you a code to unlock it. It's a far cleverer design, but in practice it's much less usable. It makes a big difference that you never just stumble across a rack and think "hey, I could be biking now." You have to apply more intention to the process, which reduces the convenience.
The real test of all the systems is how well they work when you stumble out of a bar and want to ride back to your hotel. Paris wins that contest, hands down. The NYC system looks like it is modeled after London, which isn't surprising.