I would have to say there would be multiple factors...
1)
Age: Do you have history of the buck to have some clue as to how old the buck is? If you know the buck is 6+ years old there is a chance that his rack may be at his peak...
2)
Killable: How killable is the buck? Daylight pics often? Or is the buck a ghost? If it is a buck that never sees the light of day, maybe you are best off taking the chance you get.
3)
# of Target Bucks: If you have more than a few target bucks you could maybe afford to pass on buck that is broken up.
4)
History: Do you have a history with the buck? Cams or up close and personal? If it is a buck that frequents the property often, there is a good chance he will be around next year (assuming he doesn't get harvested by others). If it is a buck that you have very little to no history with, your odds of seeing him again are probably pretty slim.
Here is a buck I harvested this season...
Now check out a couple trial pics of him from a neighbor a mile away in October...
Notice my buck had broken off each of his split brows (3" ea), tip of his left beam (1.5"), his left G4 (2")...for a total of about 9.5" roughly.
I had him rough scored at just over 169", so not broken he would have grossed around 178"+.
TRUST ME, for the opportunities I have I would never even think twice about passing up a buck going over 150" with a broken rack...but in light of others that have greater opportunities at many big mature bucks I would base it on some of the points made above. For me, I knew this buck was at least 7 years old, and his rack actually peaked in 2010. We usually get 1-2 pics a year of this buck on our property (home is about a mile west of us), whereas neighbor gets a couple hundred. Neither of us had a single daylight pic of this buck. Neighbor had 1 single daylight pic of his all of 2011...Needless to say this buck was a ghost. Taken all these things into factor, I would say drill him regardless of the broken tines...
-Mark