I've owned the older model and they are vastly different. But you already knew that. What makes the new Tucson especially desirable is the DCT transmission. It makes it fun to drive again. The engine and transmission seem up to the job and should be better than your current model.
Having said all this, which is not new, I would suggest you look through the internet using all the sources, like Cars.com, autotrader, ebay, etc. and get a realistic idea of what they are selling for. The range can be considerable. Don't know I would wait for the end of the year to arrive. I'm guessing most of the 2016s Tucsons with the 1.6T and DCT will soon be gone. There are a number of the ones with the 2.0 and regular automatics out there however. I'm guessing you want the Turbo.
The 2017s so far as I can see are almost exactly the same as the 2016 model except for the year on the title.
I would make inquiries to several dealers via internet and see what materializes. TrueCar is useful here in that you will get dealers who will provide the price and a "certificate" for the new car.
Here the catch, however. You are trading in a car. In order to compare apples to apples and not apples to elephants you need to know two things. You need to know what you can buy the new one for outright and you need to know what you are actually getting for the trade-in. They cannot be intermingled or you won't have any idea what you are actually paying. I would recommend using one of the valuation sites like NADA to determine the value of your car. Print it out. Then go to TrueCar and see what the new one can be purchased for. Then you should subtract the difference (taking into account the rebates, etc.) and that is what you should pay. If you go into the dealership cold, you will be greeted by sales staff who probably don't have a clue what they are even selling and you will have to go through the flim-flam of haggling. I never haggle nor make an offer. Let the dealer negotiate with himself. You can avoid all of this prior to doing your homework. And check the comments of customers who have utilized the dealership previously.
Good luck and I realize I have said more than you have asked, but if you want a good end of the year deal you might want to move up your time table. The desirable models will soon be gone. Just my $0.03 for today.
BTW, the "jerkiness" (starting out) associated with the DCT is common to all DCT equipped cars. At best it is a minor annoyance. Once underway you will appreciate the added responsiveness and kick in the pants that you would not get with a regular automatic.
Only caveat is not to use it to creep along in traffic. Use the brake and pull away normally. If you were to be in stop and go traffic, you could put it into 1st gear manually and just leave it there until the traffic clears. But don't "feather" the clutch as it can overheat just like a regular manual transmission which it is, except the clutches are automatically actuated instead of having to push on a clutch pedal.