A Chassidic tallit is chosen not only by chassidim, but also by those who are associated with a Chassidic community/congregation or trace their family lineage to Chassidic roots.
The Kmo Turkish is a common choice today. With its lining and sidebands, you feel "more tallit" on your shoulders and the appearance is very stately. Also, the lining and sidebands can extend the lifespan of the tallis.
You may notice that the thick black band near the edges is thicker and darker than what you find on a standard black-striped tallis.
Often a standard white atara (neckband) is chosen for the weekday tallis, while a Shabbos tallis is embellished with a gefluchtene atara.
Most chassidim will opt for thick, handspun tzitzit tied according to the regular Ashkenazi tying custom. Techelet tzitzit are often chosen by Breslov and Radzyn chassidim.
The Lubavitch custom is to have a second tzitzis hole on each corner. After tying on the four strings, the shamash string is looped through the second hole the anchor the tzitzis in place, which prevents them from sliding around to the other side of the tallis. Also, Chabad follows the Arizal tying custom, using all-white tzitzis.