Generally speaking, The Ezras Luach is the most authoritative source for days when to/not to say Tachanun for mainstream Ashkenzai Kehillas. The Luach Colel Chabad is specific for the Chabad-Lubavitch community (They do not say Tachanun on 19 & 20 Kislev and Mincha of the 18th beforehand). Concerning Sephardim, Tachanun is not said for the remainder of Tishrei after Shmini Atzeret (Yemei Tashlumim for Shalmei Chagiga) and for the 6 or 7 days following Shavuos (Same reason). Different Chassidic communities (Satmar, Belz, etc..) also have their own Luachs for their communities. As for Yom HaAtzma’ut and Yom Yerushalayim, Tachanun is observed to be said in the Yeshiva and Chassidic communities. I saw it brought down in the Sefer Nitei Gavriel (on Hilchot Purim) that there are some who do not say Tachanun from the 23rd of Adar onwards (as they are the 7 days Milu’im of the Mishkan). For final psak, please consult your L.O.R.
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