Esaka is where the company headquarters are, so I've always seen Esaka as the theme of SNK in general, more than just Kyo specifically. "Goodbye Esaka" is the only song to directly reference the state of the company, however.
Tears is a great Kyo theme. I prefer Goodbye Esaka. But there are lots other good ones. I'm fine with whichever one SNK picks. Although the XII version of Esaka would be a good choice, just because it's a great one that's never been used in-game. It really shouldn't go to waste.