When you're hiring a company to shred all of your paperwork which you are required to destroy either because of your own corporate policies or because of legal obligations, you want to make sure and hire a company that comes to your location. This type of paper shredding company is typically known as an on-site shredder, and they are much more secure in practice than companies which might want to take your paperwork to their own location before they destroy it.
There are a number of reasons that an on-site shredder is going to be a better selection for your company. The first of these is that when a company has to come to your location, you know exactly who is going to handle your documents. Obviously, if all the shredding is taking place at your office, only the employees that come with the van are going to handle your paperwork.
Why is this important? Mostly because you should have very person that is going to handle your documents that is outside your own organization sign a confidentiality agreement. If any information from those documents was to get leaked, you could be held liable, and those agreements provide some measure of protection against that. If they take the documents off site, you are unable to guarantee that only people who have signed your agreement are going to handle your paperwork.
Another reason to have your documents shredded on site is cost. Most people don't realize it but you can often save a little bit of money by hiring an onsite shredder and opting out of some optional services. For instance, some companies charge you extra for disposing of the shredded paper, but if you have an effective means of doing that yourself, you could save a little money.
The other reason is also a security reason, and it is simply that you can, or can have someone that works for you, watch every step of the document destruction process. When you send something away in a van to be shredded, the only assurance that you have that it is being done, and done securely, is the promise of the company that you've hired. When they have to complete the service at your location, you can see the evidence with your own eyes that they are completing their end of the bargain in accordance with whatever contract you've signed with them.