You're right, the rule is the same no matter where the "catch" takes place. The player has to control the ball all the way through the catch whether it's inbounds or out of bounds. The player in bounds has an advantage if he is juggling the ball because if he gains possession after juggling it it's still a catch. If a player has it, drags his feet then loses possession of it out of bounds, it will be ruled incomplete even if the ball doesn't hit the ground because he was OOB when possession was gained. I may not be explaining it well, but that's the gist of it. I've had to rule several times on whether a player maintained "possession through the catch". It's a difficult thing to call.
As for a player having to come down in bounds, I'm all for the rule change. It was too much of a judgement call as to whether a player would have come down in bounds or not. Now, he either did come down in bounds or he didn't. It's much cleaner and both teams know it's the rule. There is much less argument.