Well - here's the potential downside of keeping the house yourself:
Many women make the mistake of trying to keep the family home (mostly because they don't want the kids to experience more disruption). So they trade, say, their share of their H's pension and of the savings accounts for the equity in the house.
Then they end up with the house, a sizable mortgage, and very little cash. They struggle to make the payments, then pay for the inevitable repairs and maintenance (new roof, painting, plumbing repairs...).
Then there's a large expense or you lose your job. You don't have enough savings and you can't make the mortgage. The house goes into foreclosure or you have to sell it without being able to afford repairs to get top dollar. You end up losing the house equity AND you already gave up your share of the pension too.
On the other hand - if you make a good income on your own, if the house payments would be equal to or less than rent, if the house is newer and in good repair, if you would have enough savings to pay for the unexpected - then it may be a good idea to keep the house. Just ask yourself, if you were looking for a house to buy now, would this house fit into your post-divorce budget? Don't buy more house than you can afford.