Here are some details of the differences between these two bikes. I made a side by side photo which shows some clear differences that show that the TT is closer to a dual sport frame design, and the KPX is closer to an enduro frame design. I hope this provokes comments and opinions, and please feel free to post a comment...
CSC specifications say TT250 has a wheelbase of 55 inches. I can't find the wheelbase of the KPX, but notice that the front fork rake is steeper on the KPX? Just a couple of degrees, but this is useful for maneuvering in tight situations (an enduro trait). Wheelbase and rake interact to create road stability/instability, turning effort, and agility. In my experience on many different bikes, a more relaxed rake that dual sports have make them more comfortable on the road, more resistant to turning. The taller seat height on the KPX amplifies this slightly (just an inch or so), but this is GREAT for the times you decide to hit the trails. Enduros are more capable, even if a bit more work when you are riding aggressively off road, but the responsiveness is way better. This is not subtle in real world situations, but you can get used to either geometry (just a difference).
Footpeg/seat geometry is different:
The cradle of the seat (lowest position) is farther back on the TT and it is a deeper pocket (holds you in place). This is exactly what I experience on my Bashan Storm. It is a dual sport frame, very comfortable but holds you in place. This pocket is comfortable unless you want to have your legs less bent at the knee. I would bet that there is more distance from the peg to the seat on the KPX.
The cradle of the seat is more forward on the KPX wrt footpegs, BUT the seat is flatter so you can choose seating position while you are riding on the highway (can relieve stress), and also allows you to put your weight where it is needed when you are off road. Hardcore enduros don't even have that slight cradle you see on the KPX!
The footpeg position on the TT is farther forward compared to the cradle of the seat (again, more road oriented). Bikes that are known for their agile response, like most BMWs and sportsbikes have the footpeg more directly under your seat. It promotes more upright seating position This is better for your back, and puts you in a position to make quicker changes. Cruisers are the exact opposite, footpegs way forward, handlebars farther back, which is HARD on your back, and prevents quick turning in a bad traffic situation.
The position of the rider on these bikes with respect to front/rear axels is different. I think the swingarm pivot is farther forward on the KPX, but it may have a longer swingarm. If the swingarm pivot is really farther forward, this is another clue that KPX is more of an enduro. Certainly, the cradle of the seat is farther forward on the KPX.
If you get a chance to ride these bikes, you will experience and recognize these differences.