I understand that Tibetan Buddhism accepted both polyandry and polygamy, as well as at least one sect of married monks / nuns.

Also that the polyandry was normally one woman marrying a number of brothers. Not sure if the reverse was true for polygamy.

I have always assumed that this acceptance was tied into social conditions. A massive percentage of the population was dedicated to monasteries by its parents - monasteries had stores of food and large communal lands and herds which meant they were much more able to look after a number of children than any one family. Most monks and nuns being celibate meant that you could keep the overall population down. Some being allowed to marry gave a degree of generous forgiveness to the human weakness in us all. And those polyandrous arrangements outside the monasteries kept the family holding in one shared lump, whereas medieval English hereditary division left everyone with a too-small share so they could all starve together! Not a recipe for social harmony!

...come to think of it, sibling-based polyandry fits nicely into Darwinian genetic 'altruism' (as per Richard Dawkins' books) as a population-control method. It limits the number of children 2-5 brothers can bear to the offspring of one woman, but still gives them all a guaranteed stake in raising and caring for those children. Consider brother Albert. If the children are his, they have half his genes. Worth investing in their future to protect his genes. But if they are not his, they are his brother Bert's (or Cuthbert's, or Dilbert's). In which case, since Bert (or Cuthbert, or Dilbert) shares half his genes with Albert (yeah, I know, not guaranteed, but on average and that's the way Dawkins calculates it), the children have one quarter of his genes. So still worth Albert protecting them and their future.
So genetically, from a male point of view, polygamy works if you have lots of resources and can support more than one woman and her child-bearing capacity. Sibling-based polyandry works if resources are scarce and you will need to club together to support even one woman and her child-bearing capacity. From the female point of view, the choice is between one very well-resourced male - but you might have to share him - and a pool of more less well-resourced male.

I guess biandry doesn't give enough advantage in most situations to be worth it for the woman? The worst of both choices rather than the best?

...none of this is meant to offend anyone' religious / ethical / egalitarian / feminist / masculist principles, by the way. I just happen to think Dawkins does great analysis of how our genes drive us to achieve their goal, and I'd never thought of applying it to polyandry before. As far as I'm concerned, live how you like, just try not to judge anyone else or destroy their lives...