I'm going to go with what may be perceived as the lesser of the two/three players who are the front runners for this question. I believe the biggest loss will be Andrew Ladd.
I can see how many will assert that Byfuglien has certain characteristics that may put him ahead of Ladd, especially in the Power Forward department. And how Kris Versteeg has more honed skills in the sniper department. But Ladd has his own abilities which I believe have been underrated for many years, at times, even by me.
All these players are still young, Versteeg being the youngest, followed by Ladd. But Ladd is by far the most experienced, having played the most regular season games, and the most playoff games, while amassing two Stanley Cups during that time. Now some may argue that he may not have been the so-called "bee's knees" during those runs, but every member plays a roll, and his is often the grinding pest. He is very skilled at taking opponents off their game. Ladd has many of what some call "intangibles", being a good hitter, team player... not to say that Big Buff and Versteeg aren't.
Ladd amassed more points than Buff, and only 6 fewer points than Versteeg, despite playing less total minutes than both. Ladd saw little PP time (36 sec/g) and little PK time despite having the skills to play both ends of the ice.
And although he doesn't have the best points/game of the three (Versteeg) one other point I would like to bring up is how replaceable each player is. With the emergence of Troy Brouwer as a younger and cheaper Power Forward than Byfuglien, and right wingers Hossa and Kane above RW Versteeg on the depth chart, Versteeg is not as valuable on Chicago as he would be on another team.
On top of all things, Ladd is the only natural Left Winger, leaving a team with a plethora of RW. That is more significant than some realize.
In the end, I believe that Andrew Ladd, a 24 year old 40 point scorer, 2.35 million dollar left winged 3rd liner is the biggest loss for the Hawks in this off-season.