What's the value of learning "Chitas" compared to any other daily Torah study?
Side question: If it's so important, why was it introduced only recently?
R' Zev Dov Slonim compiled a booklet that collates various sources that talk about the advantage of learning Chumash, saying Tehillim, and Learning Tanya daily. The booklet is also included in the Chitas sefer, published by Kehot. The footnotes on Sefer Haminhagim's entry on Chitas discusses this as well.
Here are some of them, see sources inside for more:
With regards to Chumash, from here:
On Tehillim (see here for who split it up into a daily portion and why):
ויהי חתת אלקים על הערים - בראשית לה:ה
On the above Pasuk, R' Zevin relates a story titled "The Secret Weapon" in "Sipurei Tzadikim al hatorah" as follows:
Learning Chitas is something that is in the realm of every Jew. Before the revelation of Chassidus, "learning" was limited to the Yeshiva Elite and the average Jew was not able to learn Torah. Why was it only until recent that such a formula was established? This I do not know but Chitas in one way or another was done by Chassidim before the Rebbe Rayatz (6th Lubavitcher Rebbe) set up an official system.
Chumash with Rashi has been learning for hundreds of years and is a topic of discussion in the Shulchan Aruch as to if Chumash with Rashi fulfills the Torah requirement of "shnayim mikra v’echad targum" Learning the text of the weekly parsha twice with the targum.
The simplest Jews have been saying Tehillim for hundreds if not thousands of years. One of the reasons being that while there are opinions that a person must know the words of Torah he learns, this is not the case with Tehillim as simply reciting the Hebrew has a power on its own which is why 75% or more of our davening is from tehillim.
Tanya while a new Sefer is nothing new as the Alter Rebbe says in the very beginning all he did was compile sources into a small book.
What is the value? If you find value in learning Torah then there is a great amount of value. If you do not ascribe to the Chassidic value of learning that is available to all of Klal Yisroel then your question should be reworded to whether learning Chitas is a good use of your time instead of learning Gemara with Tosafos and Poskim.
As a Chasid, I would say for any Jew it has immense value.
It's more than just learning. It's also a connection to the Rebbe.
This perhaps can answer both your questions.