"Is a display port connection going to give you a better picture?"
Just to make it clear: back in the old days when the signal went to CRT monitors in analog mode the quality of the signal could have an impact how good picture you got. Nowadays as the signal is purely digital the signal quality is not really an issue, if the data gets through there will be a picture, if the data is corrupted there will be no picture. You won't notice any difference in picture if the resolution and color depth stay the same, no matter which of these digital display connections you use. The picture quality is set by the quality of you display panel or the quality of the signal feeding device, not by their digital connection.
It's just about the bandwidth that the port characteristics and cabling can support that sets the limits in supported resolutions and content, such as audio.
DVI max. 2,098 × 1,311 @ 60Hz
HDMI max. HDMI 2560×1600 @ 60Hz (+HDCP)
Displayport max. 3840 × 2160 @ 60Hz(+HDCP,+DPCP)
Just a very simplified summary.
-C+