DisplayPort (and mini-DP, they are basically the same) will in general support higher resolutions than HDMI, and in my opinion it's a better physical connector as well. The HDMI plug design sucks.
Thanks. I have a Moshi mini displayport to hdmi adapter. However, when I plugged in my MBP 2010 17" to my 65" Samsung 4K TV at home, nothing showed up even I closed the lid. I tried to change the resolutions of the TV but it did not work.
If I buy 40s" TV as an external monitor, they only have HDMI. Samsung does not say if it is HDMI 2 but I suppose so. If I buy computer monitor, they have both minidisplay ports and hdmi ports. There are many complains about the Philips 43"'s burn in issue. I hesitate to buy it. So, I am thinking of TV.