I think either one would be a good choice. They seem rated pretty close to each other in specs, so I'd say you're comparing models that are pretty close. The 25 series from Branson was discontinued in US. I think a lot of that had to do with having a nearly identical model in the 20 series. The main difference was the 25 series came with a lot more "stuff" as standard features than the 20 series. These would have been options that you could order separately on the 20. So when folks were out kicking tires, looking at the 2 side by side, they looked nearly identical, but the price was lower on the 20 series. At least until you started ordering up the additional options anyway. I don't think enough dealers put in the effort to lay out the distinction between models, so the 25 sales withered on the vine.
Strictly my opinion.
Anyway,
It looks to me like the specs between are pretty close, bare chassis weight is nearly identical, Kioti gets a bit better on FEL capacity (but you have to be careful here on how the different companies "rate" the lift capacity), same with 3pt hitch, the Kioti is a bit higher lift rating on 3pt arms, but you also have to watch how these are rated. Some brands like to play games with how they rate these.
I think they're close enough to be a wash. So go test drive both units, look at the features, cab layouts, controls and ease of use. Look at the little things, like are both lower 3pt arms adjustable (they are on the Branson). Tractor Data says the DK comes with 2 rear remotes (or is it one?-not sure now). The Branson 25 comes with 2 (mine did). The dual HST pedals are farther apart on the Kioti, make sure this doesn't bother you in your test drives.
The Kioti appears to have some features that the Branson does not, and vice-versa. Only you would be able to tell if these are important ones (to you). Kioti has a rear external 3pt control lever as standard. That is awesome if you switch implements with any frequency, but if you want telescoping 3pt arms they are an option (weird). . I wish the Branson had that external 3pt lever. Kioti also has an "optional" mid mount pto. May or may not be useful to you? But the Branson doesn't offer that. Kioti has a rear window defroster, which is also pretty cool, but the rear window wiper is optional (again, weird). Side mirrors and a front brush guard are standard on the Branson, but optional on the Kioti. A "7 pin" connector is standard on the Kioti (I assume they mean for a trailer light plug?), but not offered on the Branson. The Branson comes standard with split brakes and a rear diff lock. I can't tell if the Kioti offers these or not (either standard or optional).
There are other differences, mostly minor ones, which may or may not be important to you?
You should test drive both models as much as the dealers will let you get away with. If you have specific 25 series questions, I can help further if you want. I am one of the ones that had issues with the Branson emissions system. I fixed mine by removing it. Now it runs and drives exactly like a pre-emissions tractor. No computer, no active controller, nothing.