People usually compare him to Zetterberg which I think is actually pretty fair both stylistically and for talent. He's a smart player that's responsible defensively, is dedicated to proper positioning and doesn't sneak away from his responsibilities for breakaways. He uses his body well to carry the puck but has flashy skills to beat guys if he needs to. His shot is good and he finds his teammates with good passing. Right now he's too light for the NHL but besides that he's ready in every facet of his game.
Obviously we don't know how good Hischier is going to be (or Fiala for that matter) but I'd expect him to be better than both of those guys. He'll be a top 6 C in the NHL and probably will play on the first line.
I can see some similarities to Henrik Zetterberg in the way that they protect the puck and make creative plays, but they are also not very similar in many ways.
Hischier is a far more explosive skater, and he relies on his skating more than his hands. In fact, I would say that he handles the puck a little bit loosely at this moment and uses his skates to keep control of the puck. He needs to refine his stick handling abilities -- if he does so, he will become a dangerous threat any time he has the puck. At the moment, I would say that he won't often deke around players with his hands alone, but instead pushes the puck around the opposition and explodes past them with his body to retain possession.
If one compares his game in January to his game in March, they can see some significant differences. He was far more assertive with the puck on his stick in January, and he moved better. If fatigue is a factor, then one simply has to refer to his performances in January for a sense of the type of game he can play.
There were games when he did something every time he had the puck; for example, in the January 15, 2017 game against Victoriaville, he carried the puck out of his own with speed and set up the offensive zone entry at least a half-dozen times. He had all sorts of chances to score, and notched two goals. In his first game back from the 2017 World Juniors against the Wildcats on January 6, 2017, he dominated possession in the offensive zone and all game was skating around players, beating players to the puck, and taking pucks away with his quick bursts.
He has had several games where he has played at that level. Without question, a major element of his game is his skating ability; it allows him to create offense out of nothing and pressure his opponents aggressively; he uses his speed to create space between himself and the opponent when he has the puck, and to close the distance on them when they have it. If he could tighten up his puck-handling, he would be an even greater threat.
Hischier has been compared to many different players, and some are less precise than others: Andre Tourigny likens him to Zetterberg, John Moore and Ben Kerr (of Last Word on Sports) have compared him to Pavel Datsyuk -- Moore also compares him to Joe Sakic --, Steve Kournianos has compared him to a young Steve Yzerman, while Craig Button originally compared him to Sam Reinhart but has revised his comparison to Zetterberg. In their preseason preview of the 2017 NHL Draft, The Hockey Writers compared him to Sidney Crosby. Swiss scout Dennis Schellenberg, meanwhile, coined the nickname "Swiss Connor McDavid."
I compare him to a young Pavel Bure. While not entirely the same -- particularly with regards to Hischier's very disciplined defensive game -- they are similar in terms of their means of generating offense, their fearlessness, explosive and agile skating ability, tenacity, and grit, their breakout control, zone entry, and quarterbacking ability, as well as many of their other tendencies. They both play powerful games. At their best, they are all over the offensive zone making plays, supporting the puck, and drawing the opposition to them to open up lanes; they also know when to lurk and sneak around to surprise unsuspecting opponents. They also often start at the right point on the powerplay but like to move around the offensive zone. Hischier doesn't generate nearly as many breakaways as a result of generally playing lower in his own zone at even strength, currently not having as much strength to drive to the net and gain body position on the defender, and perhaps less of an aggressive instinct to charge up the ice as early; his Mooseheads teammates also tend to rely on him to start the breakout, and rarely spot him with a crisp stretch pass whenever he charges up the ice to lead the rush -- he does have the occasional breakaway, but there are also many missed opportunities when he ends up circling back as a result of a sloppy breakout. I see more breakaways taking place at the NHL level, as his teammates will be skilled enough to give him a perfect pass whenever he leads the transition. Hischier doesn't handle the puck quite as tightly as Bure did, and his shot doesn't have the same level of power, but there are many similarities in the ways that they generate offense.
If his name was Nikolai Khishiev, it would be the natural comparison based on nationality. Ironically, Bure's family is of Swiss origin.