The Mexican government is no longer one monolithic organization. Once the PRI lost power in 2000 after having a virtual monopoly for 70-something years over Mexico, the government has been a lot more divided... much like how the cartels are much more divided. The old systems of bribery and corruption began to break down because people didn't know who to bribe and different groups started competing for power. So there seems to be tons of infighting now and the corruption is a lot less under control and more chaotic than it ever was. Essentially, controlled corruption under the PRI until year 2000 to total anarchy corruption now.

So, "the government" can't really prefer any cartel so to speak because the government is not one specific group. It's safe to assume all of the major cartels have powerful politicians and government employees in their pocket.

But generally, a lot of the old guard PRI politicians seem to be aligned with the Sinaloa cartel, who tend to be looked at as the more old school smugglers, as opposed to the military-like groups like the Zetas and CJNG. But, it would be wrong to assume the entire government is behind the Sinaloa cartel. The situation is far more chaotic than there being some invisible hand pulling the strings behind the scenes, controlling everything.