I imagine it would be much like the many other fantasy genre games that come out today. Flashy and interesting to a point, but nothing truly amazing that will cause it to stand out in any significant way whatsoever. There are actually quite a few hack and slash adventure games that come out every year and while some are fairly successful, they very rarely reach the level of popularity that Zelda has achieved.
Fable, God of War, and Elder Scrolls come to mind but those are still somewhat building on previous successes from older consoles. Zelda coming out now would not have the long history and nostalgia that comes along with it. I'm thinking it would come and go fairly quickly like Heavenly Sword or Impressive and a fun adventure, especially for something Nintendo has released but ultimately meh, off to Gamestop for the next title. Something like Twilight Princess or Wind Waker would not really stand out too well as a medieval action RPG among all the others if it had no history behind it. Along with no history I can see the games being much simpler in terms of story and gameplay. It would be the very generic pseudo-medieval fantasy world that we have seen before so many times in the past. No greater history for Hyrule, no established mythology, everything would be very basic to introduce just this game, not series, to players.
Also I would have to wonder just how modern game would play out if Zelda was not there in the early days to introduce non linear exploration based gameplay. Almost every game on the NES maintained the standard gameplay style of level 1, defeat boss, move on to level 2, repeat. Without Zelda in 86' it may have taken much longer for a video game company to introduce this type of design to players. This would have an effect on many other free roaming games that we have now such as the GTA series and the many knockoffs that were created in response to it's success.