This, probably more than any issue in climbing, has generated more discussion, heated debates, and vitriol (especially on the internet) than any other issue in climbing. Both sides (lower vs. rappel) are equally ardent in their belief that their way is the One True Way. Unfortunately, both sides are wrong.
My rule is simple: Climber's choice. You should choose the method you prefer and believe is safer, and you should do it the same way each time to minimize the chance of a serious climber error. (You should still know both ways.)
If you are the last climber going up and will clean a route, it's important to tell your belayer what you intend before you leave the ground. This way, both parties have a clear idea of what will happen. This can be helpful if communication is hard from the top, and decreases the chance of a miscommunication.
When you get to the top, your command to your belayer should be clear and completely unambiguous:
- "Off belay": I will rappel, you can take me off belay and go do something else.
- "Slack": Just give me slack (for a lower). I don't say "in direct" because some belayers may misinterpret that to mean off belay (I've trained that out of anyone that belays me regularly, but you never know).
The tradeoffs roughly fall into three categories:
- Speed: lowering is significantly faster.
- Safety: when done correctly, both are equally safe. However, lowering tends to have slightly fewer steps where you can mess up and more places where you can "double check" yourself.
- Ease when cleaning draws: lowering is significantly easier because the belayer controls your descent and can help pull you back into the wall on steep climbs.
- Equipment: rappelling puts slightly less wear on the fixed anchor and the rope. Most rap-vs-lower arguments revolve around wear and tear on the anchor; as long as you're not top-roping directly off the anchor this is a non-issue as far as I'm concerned.
Personally, in regularly visited areas I almost always lower. It's my choice, but if I'm belaying someone who wants to rappel I do as they wish.
Some exceptions to the "climber's choice" rule would be if the area's guidebook says otherwise, or if the local climbers all rappel ("do as the locals do" is always a good rule of thumb). In seldom-visited areas, I generally rappel.