I would have to say that you can't really measure crime on a simple "size" scale, so neither works; you need to establish what aspect of crime you are measuring, and then apply an appropriate adjective. In this case I think you are referring to which crime is committed most frequently, so you might say

Theft is the most common crime in America.

Depending on what else you are measuring, you may have to get very wordy; if you want to refer to how much monetary value is lost, for example, you might say

The crime that costs its victims the most money is theft.

If you're talking in terms of numbers, then largest or biggest could be used.

Office place theft cost American companies 3 billion dollars in 2016. This dwarfed shoplifting, which in comparison, cost approximately 300 million dollars.

This makes things like stealing office supplies the largest crime in corporate America.

Although in this case, I'd probably use "largest/biggest problem" or the "largest source of lost profits".

In general, largest is perhaps slightly more formal, but there's not a large/big difference between the two.