What differences if any would the different monitor connections provide?
Thunderbolt digital video output
Native Mini DisplayPort output
DVI, VGA, dual-link DVI, and HDMI output supported using Mini DisplayPort adapters (sold separately)
HDMI video output
Support for 1080p resolution at up to 60Hz
Support for 3840-by-2160 resolution at 30Hz
Support for 4096-by-2160 resolution at 24Hz
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John Kueck
Hard to say without knowing if you are referring to the cables, the output source (computer) or the device (the screen).
For instance, you could have a screen that accepts Thunderbolt input and not only gives you your display, but also USB ports, audio, a camera, and even power. Thunderbolt can carry all of that. However, Mini DisplayPort is really just video. The same with DVI, VGA and HDMI. However, there are differences, like HDMI can carry audio too in the right situation.
I'd be better able to help if I knew the actual situation or options you are deciding between. In most cases if the screen takes Thunderbolt, then use Thunderbolt. Why wouldn't you? If not, then mini DisplayPort is pretty standard. If that's not an option, then HDMI is usually better than DVI and VGA.