I’ve tried all three. The bandaging method was fun to do; but I was less than satisfied with the results. I may have made some mistakes along the way, since I only tried it 3 times; but I found the rind was thicker, and the cheese itself was not any better.
Waxing is a messy job, cleaning up afterward is inevitable, and there are some drawbacks. The problem I was encountering was that the wax tended to crack over time requiring regular close inspections and repair jobs.
I have gone to vacuum sealing because it is easy, efficient, and its great to actually see the wheel itself as it ages. There is no rind to contend with afterward either. I have noticed no denigration in the quality of the cheese versus either of the above methods.
As to breathing, a good coating on the bandage and a good wax job will result in very limited breathing if any at all to my personal way of thinking.
In the end it comes down to what you personally prefer. Use one or all of the methods and develop your own style - and enjoy! That’s what it’s all about.