On the face of it, this should be an obvious choice. Boards should usually take the higher price. But this particular situation goes deeper.
One big reason why Bain/Blackstone can pay a higher premium is because they are not looking to sell the Asia assets. Such deals would result in a massive tax bill for Yahoo – multiple billions of dollars – given its puny cost basis ($1 billion for Alibaba, nothing for Yahoo Japan). There has been some talk of Yahoo doing a "cash-rich-split-off" to avoid such taxes, but such a maneuver can only be done in concert with Alibaba and Softbank. If those two companies are working on a majority bid, why would they enable the minority bid to succeed?
The counter-argument, of course, is that Bain and Blackstone would offer Yahoo little operational "value-add," as neither is known as a particularly tech-savvy investment firm (at least compared to Silver Lake or TPG). Legit concerns, as would be the likely use of leverage. But everyone I speak with believes that Yahoo's primary problem is a lack of focus. In other words, it needs to stop lots of extraneous efforts and refocus on its core of advertising via content and commerce.
Sometimes being known for slashing and burning is a bad thing, but sometimes it's just what the doctor ordered. Yahoo is probably in the latter category, and insiders don't see it happening -- at least not as effectively -- if Yang remains a 10% equity holder and board member. Moreover, there is a sense that Yahoo could operate much better as a private company than a public one, at least in the immediate future as it tries to restructure.
Speaking of the board, that's another issue I discussed yesterday in a blog post: The entire thing has to go. It leaks like the Titanic, making it reliably unreliable. A majority takeover accomplishes this objective. The minority deals do not.
It remains quite possible that Bain, Blackstone and its Asian partners won't make a bid. After all, we've been hearing about an Alibaba bid for eons and it hasn't yet materialized. But if it does arrive, I really don't see how Yahoo's board can turn it down for any reason other than self-preservation as directors of a fading public company.