Those two carbs you linked are completely different in how they work.
One is a constant velocity (CV) and the other is manual, some older folk may call it sligshot linkage.
Either style can be used on the same engine and OE manufacturers often did just that based on the market/country they were to be sold in. As for the 250SX, I'm not the one to say. You can look at what other countries got on their trikes, but whatever hit the North American market is probably the same, as in either a CV or manual, but not both.
As long as a carb is properly sized, in good condition, and tuned correctly, there are often minuscule gains in power to be had between various designs, especially on a stock engine. The engine itself limits the power available, by compression and camshaft to a large degree. A 'performance' carb may feel more powerful, as in better acceleration or at least the perception of it, but max power will be about the same without doing internal engine modifications. It's like when a carb with an accelerator pump is used and the majority of people think it's more powerful, when time and time again, dyno results say otherwise. Faster accelerating, sure, but not necessarily more powerful. That becomes obvious during something like a hillclimb or heavy towing, which will load the engine beyond the point of acceleration.
There are exceptions, especially if an OE carb is a particularly bad design, but that's not the norm since probably the 1970's, at least with Japanese carbs. No tickling the Amal. That's an actual term and carb brand, if you want to look it up. There are aftermarket carbs that offer actual power increases, but you'll run into a lot of issues you'd probably rather avoid, then there's the price.
On a stock 250X, or even a mild build, either will probably work well. The CV carbs tend to soften the power curve, but they're main objective is to compensate for large elevation changes without having to rejet. A manual round slide carb, slingshot, typically has better throttle response, feels more powerful, but will complain more during changes in elevation.
Either is fine depending on the use. CV carbs tend to make better work/trail engines, because they're less sensitive to rapid throttle inputs. It makes the ATV easier to ride as far as not being as susceptible to jerky throttle inputs. In technical terrain, that can be a benefit, even for an experienced rider.
For general trail riding and improved acceleration, a basic mechanical round slide works pretty well.
Really, it isn't something to overthink. Just use whatever is near stock, tune it well, and call it a day.
Again, I don't know, I'm not a 250SX guy. The above is general small engine carb related, not specific to your needs or wants. Whether either carb will fit your trike is unknown to me.
A whole lot of people overthink the carb thing, expecting some kind of miraculous engine transformation, but what they often end up with is less money and an engine that runs worse than stock, and to add insult to injury also uses more fuel.
The story of three wheels and a man...