Very exciting trip Kaapsedraai!! I live exactly 100km from each of these parks (between the two) and they are both amazing! Wilderness is also very special, the birding is out of this world!!
I would spend my extra day at MZNP. But it depends what YOU want and what YOU are interested in as to which park will suit you best.
MZNP has amazing bird life which will keep you facinated for hours on end. It also has unique species like the aardvark and aardwolf which you will struggle to find in most of the other parks (the last time I was at MZNP for the day I saw four seperate sightings of aardwolf!). I find that MZNP has a higher diversity in terms of both its fauna and flora! If you have a 4x4, the park has three new 4x4 loops which are amazing, you really get up close and personal with nature and the sightings are incredible because they each take you to different habitats (so you see different species on each loop - birds, animals, vegetation and geology). The accommodation at MZNP is incredibly reasonable for what you get and the atmosphere is awesome in winter. You have indoor fireplaces, heaters, etc. and you also have a good chance of seeing snow on the high lying mountains in the park (seeing a cheetah walking in snow is quite special). The MZNP has a special charm and a more rustic, less commercialised feel to it!!
Addo is also great though, and you have a good chance of seeing Caracal and bushpig (another two species which are hard to find in other parks). Addo gets cold in June, but it's more of a damp cold than MZNP, I am sure that the Safari tents are equipped with suitable heating and blankets (I don't know, I've only stayed in the chalets). Addo also has some great birds, but it is not nearly as diverse as MZNP, but the water birds and thicket birds are all beautiful. Again, it depends on what you personally prefer as to which park your extra day will be well spent in! The ellies in Addo are very special, but I'm more of a diversity and the-more-species-the-better type of person so I get tired of seeing the same large herds of ellies everyday (I know it sounds a bit harsh)! However, because the fences have recently been dropped between the two main game viewing section of Addo, the diversity of the viewing area as a whole has increased (although I can't really comment as to how much)!!
I don't know if I've made you decision more or less confusing
But I hope this helps!!
Have a fantastic trip