The Joe Jr is taller than the mini max and will hold more lump. Its only a couple inches shorter than the small green egg. When I put my junior in the same table the small was in I had to add a paver and it still sat a little lower. The diameter is also a little bigger as my woo moves around much more in the KJ. I have not cooked on a mini max yet so I can't help you there but I will tell you 2 weeks after I got the KJ I got rid of my small egg.
I just wonder what the heck he was cooking on that caused that much smoke. I could light all my smokers and after the first 45 minutes or so once they are dialed in there's very little smoke coming out and no way it would cause someone to choke 2 houses down.