Well depending exactly what year of truck your looking at will changes things slightly, and the prices are sky high on all of them currently.
But I assume no matter which year it would be a k2xx correct?
So the 2015-16 trucks will be the LML motor still. The 2017-2019 will be the L5P motor. They will all have the 6 speed Allison trans in them.
Both are the same chassis, but the motors are different. The LML is still close to the original duramax design way back in the LB7 days. The main potential problem area that is unique to the LML over the L5P is the cp4 injection pump. They can fail, and if they do, they can wipe out the entire fuel system. Both Ford and Ram have the same issue since they use, or used the same pump design. But use quality fuel, a good additive, and a lift pump, and you'll likely be just fine.
The L5P is also free from flaws like anything else. Fuel system issues exist on that platform as well. Injector issues are fairly "common". And common isn't really the right word, but it does happen. Same thing with the fuel pumps. Now that the L5P motors have been out there for a while, I'm seeing reports of fuel pump failures, not all too dissimilar to the LML.
Another thing to think about is any modifications you may want to do. The L5P has a locked ECM, so any tuning you may want to do, will need a new unlocked ecm, which isn't cheap (prices have been dropping slowly), and that means it needs its own proprietary data link adapter and software.
The LML on the other hand, you can tune all you want just like the previous generations. Parts pricing as far as aftermarket stuff goes, is still cheaper for the LML than it is for the L5P, and LML parts are much easier to find than L5P parts as well. This should continue to get better though as time goes on, and more and more companies make more and more parts for them.