It's true that both are correct, but when you say "we used to" it means you did it in the past (and most likely not that much anymore). And when you say "would often" it does not only mean you did it in the past, but you also did it often.

Both are correct.

Both sentences basically mean the same thing. The word often is used to show that you played together many times. Where the second sentence would mean more like we played once or twice (not many times).