So for grins I re-ran my 2016 return using the new rules. Federal bill ends up being about 8% less and I think it'll play similar for most people.
Playing with a couple different scenarios, I was thinking about the impending blue state deduction apocalypse. If you're making a certain amount of income, chances are your triggering the AMT anyway, so property and state taxes really don't matter from a deduction standpoint. There are probably a lot of households in big metros that fall into this category and for them, they should see a decrease in their tax bill.
That means the folks that are really going to take it in the pants are those who have overextended themselves from a real estate perspective (I don't mean this as a disparaging comment. I realize in certain parts of the country, the only way to own a home is to overextend.) They haven't had enough income to to trigger the AMT so have been realizing the full state/property deductions and because of state/local rates they're going to hit that 10K ceiling fairly quickly.
Disclaimer: I am in no way a tax expert, so could be off base and I only looked at Married/Jointly.