I live on the Border and have travelled far into Mexico a great many times. If you can get your piece into the country, but wind up having to use it and are caught, you're in a world of hurt. If you get in any kind of trouble, which can be defined as attracting the attention of the police (you don't have to be doing anything wrong. They just want your money) or other criminals (they are abundant), you're in a world of hurt. Mexico does suck, especially with a drug war going on that rivals those that have happened in Columbia.
If you feel you may need to defend yourself there, go somewhere else. Otherwise, don't pack anything and stay in well lit and well crowded areas.
Mexico is beautiful, but very dangerous.
PS
Never go to Mexico City.