They will both need batteries than need replacing and the mouse will probably be heavier to use due to the batteries. I changed my wireless mouse for a wired one because of weight and battery use. A pair of AA Duracells lasted about 2 months. Keyboard I've had no probelms with and still on original batteries after two years.
I use a Fujitsu-Siemens wireless mouse. It does weigh a bit more but it has these advantages:
Much more freedom of movement than a corded mouse.
Works with ordinary and rechargeable AA batteries
The receiver/charger is connected to the mains so it will charge even when the mains is off.
If you forget to charge it, you can use any other AA batteries, and if you haven't got any, you can take the cable from the charger and connect it straight into the mouse so that you can carry on working.
I can't see any advantages at all in a cordless keyboard.
Maybe you would like a similar mouse to the one I use. It`s a cordless optical, the mat plugs into usb port, the mouse is battery free and gets it`s power from the mat. I`ve had mine for over a year and I wouldn`t have any other type now. If you type cordless battery free optical mouse into google, you should come up with several reviews, and sites to buy from. Never used a cordless keyboard so can`t advise on that.
One thing to note: some manufacturers' mice and keyboards can have some small delay on them (for whatever reason), so there's a slight pause between pressing a key and the character appearing on screen.
I know Microsoft stuff used to do this (perhaps it's fixed now), but as far as I know, Logitech's stuff doesn't. I have their MX1000 cordless mouse, and it's excellent.