I'm surprised that no one has mentioned this...the mens rea required for a crime is not always intent. There are lots of crimes penalized for lesser mental states, even where not based off the four-levels-of-culpability model of the MPC (e.g. depraved heart murder).
And as others have mentioned, there's absolutely no utility to making the comparison.
In torts, intent means you act either with the purpose or the substantial certainty of result, say for battery, you either act with the purpose of making the harmful or offensive contact or you act with substantial certainty that your action will result in the harmful or offensive contact.
In Crim, mens rea describes the mental state to which we prescribe criminal culpability. This is not always intent, or substantial certainty (called knowingly by the Model Penal Code), as the poster I quoted points out. Some crimes have "lower" mens rea requirements: recklessness (you considered the results and did it anyways) or negligence (the criminal result never occurred to you, but it was unreasonable for it not to have occurred to you).
There's some difference between the MPC and the common law on punishing people in the negligence category, but that's beyond the scope of your question.