If it comes down to a 1st party bidding war, I'd more expect Microsoft to swoop in and outspend the field as usual. Losing Final Fantasy would essentially mean the end of PlayStation in Japan (and also significantly impact them overseas), losing Dragon Quest would seriously handicap Nintendo in Japan, plus with all the Eidos studios and properties it's really just too good an opportunity for Microsoft not to jump all over.
I doubt it comes to that though, we'll see SE sell off assets/studios first (Eidos, Taito, etc). Hell, we might see Enix divest themselves of Square entirely to stay afloat if it comes to that.
Among the first parties though, I'd say a Nintendo buyout has the best chance for preserving and growing SE's Japanese side. They already have good working relationships with most of the studio heads (Horii, Kawazu, Nomura, etc) and they're the only 1st party actually investing in Japanese developers to any real degree these days. Wada actually said Nintendo was the last the Japanese console maker too, at this point Sony's considered "western". I'd expect Fukushima, Wada and the board to favor a Nintendo purchase above the rest, though Microsoft's money would probably win out.
Sony really seems like the least likely of the 3 to secure them imo. They don't have either the cultural pull of Nintendo nor the financial pull of Microsoft, and they really don't even make for an attractive middleground between the two in those respects.