In my synagogue, Mincha ketana is always right before sunset.By the time the Sh"tz finishes, it is past sunset and there is no Tachanun. I can go to Mincha gedola with Tachnun at a different place. I do know there is a pro for Mincha ketana, being at the time of Kurban Ha'Tamid. However, I have never heard of an importance of having Tachanun.
Similarly, 2 synagogue have Tefillah, one with Tachanun and one w/o for whatever reason, is there a preference to go to the one with?