A mildly funny thing about vacant housing/everything is corporations conspiracists is they can't tell the difference between BlackRock and Blackstone. Though neither one is a hedge fund.
They are completely unrelated companies with similar names. There is nothing to compare.
Blackstone is buying houses (though it's more an effect of the housing crisis than the cause of it); BlackRock runs ETFs you can buy in your retirement fund and is known for asking corporations to care about climate change.
blackstone - private equity / alternative investments company (originally mediated M&A deals)
blackrock - primarily sells shares in index funds; one of the big 3 index managers (started as a partnership between blackstone and others... that's why the similar name)