Based on my VERY limited experience:
LEAST: NFL- A short season, lots of injuries and a fluky sport. Seems to me a good draft can quickly blow up in a team owners face and a saavy team owner that had an unlucky draft can quickly pick up on emerging free agents especially with extra time in between games to prepare.
Next least: MLB- Baseball is such a hard game to predict. Over 162 games players go cold, they go hot, pitchers go cold, they go hot, and again a saavy baseball mind can pick out the diamonds in the rough. Too much can go wrong over such a long season and a lot of the game is based on plain luck.
Next most: NBA- Its pretty obvious who the first round picks are: Lebron, AD, Kawhli, Joel Embiid, BWest, Kevin Durant (not this year obviously), James Harden, Paul Geroge, Kemba Walker, Freak etc. Basically in a 10 team league if you don’t pick up a top 15 scorer with your first pick you basically blow it. Only danger is if that #1 pick gets injured for the season you are fucked but its a rather low risk proposition. HOWEVER the challenge is in what you do the remaining rounds!
MOST impact–NHL- The NHL rarely changes from year to year. Unicorns are rare as NHL coaches are the most stringent about even the most promising prospects must earn their ice time. I looked at my NHL fantasy league and for the most part, those that drafted the best are on top. In addition hockey careers can last a long time, so even top players in their early 30s can still be big contributors. I contend that of the 4 US sports, the draft is the most important when it comes to NHL Fantasy.