Well, first of all, Bluetooth *is* RF. So, you really mean Bluetooth vs. non-Bluetooth.
There are various non-Bluetooth technologies available.
Bluetooth uses frequency-hopping in the 2400 mHz band. It was designed to use relatively little power and be reasonably resistant to interference. One advantage is that it is the only RF technology currently used for wireless mice and keyboards that is standardized across manufacturers.
A disadvantage of any 2400 mHz device is that they are competing with a wide variety of devices - wireless phone, WiFi, and your microwave oven.
Most traditional wireless mice and keyboards do not frequency-hop and use a single channel for the keyboard and one for the mouse. (Some older equipment may come with a single-channel transceiver, which can talk only to a mouse or keyboard. These are 27mHz. They compete with Citizens Band radio and some other low-power unlicensed devices. (Letsee, remote control for model planes, etc. would be one.) I've used Logitech wireless mice and keyboards for years, and never had a problem with battery life. However, some newer fancy models can run down batteries quickly. They are not interchangable between brands. Ironically, despite lacking frequency-hopping, these seem to be amoung the least affected by interference, because the Citizens Band has fallen into disuse.
On batteries - if the device has high consumption, use rechargables. If the device has low consumption, use regular alkalines. The problem with rechargables in low-consumption devices is that rechargables have a short shelf-life. Alkalines will last longer. Some devices give you no choice, and have proprietary rechargables. They do that because they are high consumption.
Some mice now use 2400 mHz, frequency hopping, but use proprietary standards - not Bluetooth, and not WiFi. There is some interchangability within the same manufacturer. For example, Logitech has compatible desktop mouse, notebook mouse, and presentation pointer. You have to look carefully at the packaging for the 2400 mHz designation. I have the Logitech MX610 left-handed mouse, which is 2400 mHz. I got it only because it's the only left-handed mouse available. It's fairly susceptable to interference, despite frequency-hopping. I can't use it when I am running the microwave oven in the next room. The battery life is very good, though I have read complaints from others.
There also are IRDA (infrared) keyboards, and these are interchangable. Not sure if there are IRDA mice.
I actually went back to a wired keyboard, as I wanted to try a Model M (not a real IBM, but the currently-manufactured licensed product from Unicomp) which I really like. It's the mouse where you really need wireless. I always found the cord to get in the way.
Frequency-hopping and mice/keyboards does not necessarily mix well. Frequency-hopping depends on the fact that if there is interference on one frequency, there won't be on another. The device randomly hops around to different channels. The problem is, if there IS interference, then there has to be a re-transmission. Works well for streams of data that can be buffered (audio, video) and OK web browsing, etc. Problem with mice/keyboards is that users expect real-time response - you don't expect to hit a key or move the mouse and sometimes have a delay.