Whether the Chicago Bulls have depth or not will depend on whether Marquis Teague or Tony Snell can prove they belong. The Bulls have five solid players to fill out the primary guard and wing minutes. Five players is enough to cover three wing positions if everyone stays healthy without worrying about the sixth guy much at all.
That said, Derrick Rose, Kirk Hinrich, and Luol Deng don't have the best resumes when it comes to staying healthy. Odds are high that the Bulls will lean on at least one more player fairly heavily this season to compensate for an injury to someone in that primary guard rotation. Tony Snell and Marquis Teague will duke it out to see which of them can be that player.
Granted, it will depend somewhat on who goes down, but it really only makes a difference if that player is Derrick Rose or Kirk Hinrich. In the case where Rose or Kirk goes down then Teague is guaranteed minutes at the one, because Snell simply can't play there.
If Butler, Deng, or Dunleavy were to go down Snell might have somewhat of an advantage in terms of filling in for that player, but the Bulls could also simply shift their rotation. Say Deng goes down, instead of Snell filling in for Deng, Butler slides over as starting SF, Hinrich is promoted to starting two, Dunleavy can play with either Hinrich or Deng, and so those three cover the vast majority of two/three minutes.
With Hinrich sliding to the two full time, Teague becomes the full time backup PG. The same basic scenario is true if Butler or Dunleavy are hurt as well. In any of those scenarios, the Bulls can play the two/three with whomever is left and keep Teague at backing up the point, or they'd have the choice of using Snell instead and keeping Hinrich at the backup point.
Of the five wing players projected to play in the rotation every night, two of them mandate Teague taking a big role in case of injury and three of them give the Bulls a choice. In that sense, Teague has the upper hand if everything else is equal.
That said, it could be argued in an injury situation the Bulls may look to replace function. Teague can't replace Dunleavy's shooting, and Snell probably replaces Butler or Deng's defense better with his size. If the Bulls choose to use Teague and move the rotation around instead, they'll also be choosing to change the fundamental way the rotation works whereas Snell may come in and keep the status quo with a more similar skillset.
In fact, the skillset might be one of the biggest problems facing Teague. His best moments come defending PGs and attacking the basket with the ball in his hands. Neither of those skills are particularly valuable if Derrick Rose is on the court with him. The Rose factor will always limit how much development Teague can do.
Is there really a scenario where Rose is healthy, the game isn't a blowout, and Teague plays more than 12 minutes? Even with two injuries to other players in the backcourt and tremendous play by Teague that probably doesn't happen.
In that sense, while Teague has the edge to get some playing time, Snell's the only guy who could really command significant playing time with quality play if he can prove he deserves it. In a scenario where Deng, Butler, or Dunleavy is hurt and Snell is playing great basketball, he could easily carve out a 25+ minute niche for himself, something Teague won't do.
Of course, it's probably unlikely that either guy plays well enough that we worry about getting them burn but given the roster turnover coming next season, Chicago really needs to find out if they can rely on either player to fill in a valuable gap or whether they need to upgrade one or both next off-season.