Now that's an easy one! It's the wires.
Now, that said, it's a little more involved than that. There's a difference in hardware, methods, maintenance, as well as a few other nagging details.
Hardwire is what it sounds like, a wire run from a main control unit to each individual device. It is very labor intensive, however the parts are sometimes cheaper than their wireless counterparts. Over time, hardwire usually is cheaper to install and maintain, but more labor intensive, as well as the limiting factors of a building's construction may not facilitate installation or concealment of wiring. Usually, part of the benefit of hardwired systems is the fact you can mix and match devices to suit your install, with the exception of keypads and certain components. Hardwired devices also have the benefit of being somewhat smaller and more discreet when installed properly. There is also usually the ability to always update and upgrade the system as long as the wiring allows.
Wireless devices act like a small radio station and your system will have the functional equivalent of a radio or stereo receiver installed on it. The devices will have a battery (or multiple) installed in them, with the better units using a lithium battery for longer service intervals. You will for the most part be limited to a single manufacturer's devices. The devices are somewhat larger, however will function essentially the same as their hardwired counterparts. A faster and less intrusive install is also a benefit. A few drawbacks of wireless are that the devices are generally larger than a hardwired unit, require some maintenance (batteries) as well as face an eventual obsolescence when updating or upgrading a panel.
A good thing to consider is overall cost of units, wireless will require a higher cash outlay initially, as well as over time. If budgetary concerns apply, the best way to cut costs instead of protection is to wire as much as possible.
From the pro standpoint, a good installation company will survey your site and offer both and explain the aesthetic and functional differences so an informed decision can be made.