The above summarizes very well the advantages of using the Minkus worldwide pages. I very much prefer Minkus' approach of including more spaces for stamps than the Scott International pages do.
I also much prefer their organizing system which does the far more logical thing of combining all stamps chronologically instead of separating them by type which makes little sense to me. Putting semi-postals and air mails with the other stamps they way they were issued and used at the time makes good historical sense and good design sense, as well, since stamps of the same era often reflect similar design elements. Separating them the way Scott does has never made the slightest sense to me. In all the Scott albums I use, I remove all the semi and air mail pages and put them as close to their proper chronological order as I can manage so the sequence of stamps is the way they were issued and the historical events and stamp designs are where they belong. So there is a way to deal with Scott's strange organizational system even though it's not perfect.
Scott numbers and catalogues are the default today and will always be. Minkus numbers are dead and Minkus catalogues are no longer published. And of course you can't buy stamps with Minkus numbers. So that's a drawback of Minkus.
Shelf space is not an issue for me. I just get more shelves! And I find the enormous size of the Minkus binders almost comical. Ever dropped one? You don't ever want to do that. You'll be in the hospital and your binder will be in bad shape. Aren't the Scott International binders just as large? Well, yes, the large size is. But the other size isn't quite as big, so that's an advantage for the Scott International, in my book. I actually use an alternative binder which Subway Stamp Shop used to sell (no longer unfortunately), a smaller sized binder for the International pages. It's wonderful. Easy to pick up, and so on. It's much more pleasant to use. Scott or someone ought to bring back smaller International binders.
I much prefer the color of the Scott pages. The blazing white of the Minkus pages sears my retinas. I have to turn the lights down. Minkus pages are thinner and more likely to tear than Scott pages -- or at least they used to be. Maybe they've beefed them up lately.
My major complaint, though, about the Minkus global albums is their absurdly over-crammed pages. I had childhood albums that looked just like this with every inch of the page crammed with spaces. I think it's an awful look. I realize some people love the Minkus pages. They find stamps all over the page very appealing. More power to them. But I find them truly awful designs, much too crowded. like the more elegant layouts of the Scott pages.
I wish Scott had included spaces for more stamps -- and that will be the main complaint you hear about their pages. You could use the Vintage Reproduction pages, though, if you want real comprehensiveness (but expensive) and then combine them after 1940 with the regular Scott International pages. But, from about 1950 on, the Scott pages are as complete as Minkus. At about that time, Scott began issuing supplements to their International album for all stamps since all stamps were now commonly available. The rationale for limiting the number of stamps earlier was that many stamps were not commonly available so why include them. After about 1950, Scott pages no longer omit stamps as the did for the earlier years.
I have one (1) Minkus Global album, by the way, but didn't like it enough to buy more. I have 30 volumes (smaller binders remember) of the Scott International which I love.
For missing stamps, I do the obvious -- I add a blank page and mount them there. Easy solution, and if you include a few blank pages for every major country as you put the albums together, you may not even need to add many more later. Some people mount extra stamps in the margins, but I find that too messy unless it's just one or two stamps. And it's mainly for the pre-1940 stamps which with some countries involves relatively few pages compared to later pages. Annoying, yes, but blank pages are my solution.
It sounds to me that you don't like the Minkus album enough to continue with it. I suggest you go with your instincts and switch now to Scott before you mount too many more stamps and have to move them. Both albums have their limitations, as you can see. You just have to decide which ones you can live with. For me, the more elegant look of the Scott International pages wins, but I do understand the organizational appeal of the Minkus albums (which I wish Scott did) and the greater comprehensiveness. But since I've got easy work-arounds for both -- moving pages to where they belong chronologically and adding blank pages -- it's no problem.