^Piggybacking off of this, I have to admit, Gaika is my favorite live non-Kajiurago track. I know Stone Cold and whatnot are really good and popular but. Gaika is truly something. I honestly want to use it as an op/ed in my story.
My favorite live Kajiurago track including anything from Yuuka (admittedly I don't like her and only watch her live for the background vocals of Kaida/Hikaru) is very hard to pick, and so I'll list the 3 that I play most often, which are the later Zodiacal Sign performances; Madlax Mix; and the Xenosaga II image theme.
English live fave? In The Land of Twilight. It would probably be Warp, though, if they'd ever done it live. I have to admit, I only heard Warp in early February out of all the years it's been a thing, but I am now a little obsessed with it -- I wish the music wasn't so long, that song needs more vocals, and I absolutely adore the quality of Kaida's alto part and wish it was louder.
And a Kajiurago song out of all work done ever would be really hard to pick but if I were pressured under a 5 second time limit, I would say Pandora Hearts. That song is a true obsession of mine, in my dream I would like for YK to use the melody, harmony and aesthetic for my show OST. Speaking of which, I have an entire trailer mentally created to the song but ofc I can't use it because it's Pandora Hearts. However, I would actually like for Hikaru and Miss Kaida to sing it, for aesthetic reasons. That's no insult to be directed at Wakana, as my play count on her version is nearing 10,000 in my iTunes account. I sing every harmonic part, I used the song as my audition for my college dance program, just years and years of love for it. I can't even remember where I heard it, as I hadn't watched PH and I admit my introduction to Kajiura was with Mai-HiME.