Security or police, police or security...
Depending on the situation in your area, the benefits will vary.
Security can be very profitable and is usually a lot less stress. It is generally a LOT easier to get hired as security. There are usually a lot less directives and regulations to follow as security. And, there aren't any special laws written that can land you in jail simply because you are employed as security. Security can be very boring, but it depends a lot on what type of contracts you're working, and what kind of area as well. With security, you don't take your work home with you, and no one considers you the "neighborhood cop".
Law enforcement pays fair to well, and usually has great benefits. The hiring process generally involves having your entire life laid out for the hiring entity, and can take up to a year, sometimes longer. In addition to following all laws pertaining to peace officers, department regulations also must be followed. The laws are generally more lenient when it involves carrying weapons for LEO's also. Work follows you home, can cut into your private life, and the required overtime can leave very little time for your family.
I have been both, and right now I'm a supervisor and trainer for a security company. I have been a patrol officer and instructor for law enforcement agancies in the past. Currently, security fits me better. I miss police work occasionally, though. Either profession will prepare you for the other. Pay can be similar, again, depending on your area or contract.
My suggestion would be to apply to be a police officer/deputy/trooper/et al, and work as security while you are going through the hiring process. The odds are against you being hired for quite some time as LE, so you might as well make some money and get some experience while you try. You might find you like one over the other, but you can only REALLY know by doing both.