Choose a band saw on two main criteria: throat depth and cut depth. You are comparing two models with the same depth of cut, but one has a larger throat depth.
A larger throat depth gives you the ability for wider cuts. i.e., you could cut to a width of (nominally) 12 inches on the larger one.
It is up to you to decide if 10in. is large enough or not. I mean, if the question is "why would you ever need to cut 12in. widths" then I suppose you already know the answer. Other than the obvious answer of "because you want to cut to 12in. wide boards", maybe:
- You make tables from slabs you saw yourself, and you like joining 12in. segments instead of some other even-valued maximum.
- You make plywood panels for home studios, and standard 12in. panels are easier to work with. (There's a reason for a 16in. throat I guess.)
- You have the space right now, and maybe one day you might want to saw to 12in. widths. Future-proofing is a reasonable buyer's criterion.
- Sometimes you need that space for other reasons than linear space, like cutting wide radiuses with thinner blades.
I think, in general, when it comes to larger free-standing tools like this, someone will have an idea of the minimum size they need in one or more directions. The purchase will then be more driven by price, size, availability, service and repairability. I mean, why not get a 24-inch saw, just in case? Probably because it won't fit in the shop, or is too pricey. The difference between 10- and 12-inch saws will probably come down to these other criteria if you already know 10-inch throat is good enough for you right now.
Check the specs of each. Some models allow you to double the cut depth for resawing larger pieces with an attachment. Basically, you can move the guide up 6 inches or so and run a wider, thicker blade.