For most enterprise applications using monitors, DP is the way to go. DP is replacing DVI on many monitors. HDMI is very prevalent in the consumer space (televisions and high-end/gaming graphics cards) and for projectors. Both DP and HDMI seem to appear on most modern monitors replacing DVI-D and VGA.
HP appears to offer more DP considering http://www8.hp.com/us/en/products/monitors/index.html#!view=column&page=1&facet=HDMI shows 35 choices but http://www8.hp.com/us/en/products/monitors/index.html#!view=column&page=1&facet=DisplayPort shows 66 choices. Samsung seems to be a little more HDMI having 26 HDMI and 10 DP at http://www.samsung.com/us/computer/monitors/all-products . Dell is definitely in the DP camp but their higher-end monitors also have HDMI.
HDMI can be unplugged easily, sometimes accidentally, as compared to the latching full size DP connector. This can mean IT service tickets just to plug-in an HDMI cable. It just comes loose much more easily than DP.
On the PC/Macbook, it seems there are many more DP/mini-DP ports showing up than HDMI/mini-HDMI/MHL.
All this leads the DocKtor to believe that companies are better off buying monitors with DP other than HDMI if given the choice.
BTW, VGA still ain’t dead.