They're the same generally speaking, the only difference is when you want to use a super high screen resolution like on a 4K-capable monitor - then DisplayPort (Thunderbolt connector) will need to be used, the version of HDMI currently used in Mac minis doesn't have the bandwidth for it.
Since you posted this in the Mini forum, I assume you are asking about Mini's.
If that is the case, then the only Mini capable of 4K is the 2014's via HDMI at only 30hz. The Thunderbolt ports on any Mini (whether 2011, 2012, or 2014) are only capable of a max of 2560x1600.
As far as which one is superior, they are both a digital signal so all things being equal there shouldn't be any difference....
Thanks Paul, Yes I have a 2012 version I bought it right before the 2014's came out. Coin toss on whether I should have waited, but the new ones are a bit pricey for the additional ram which you cant add yourself.