I will explain a few things

:
Those two are not the only music playing shields you can buy.
The rMP3 is designed for high quality music and is, as you say, feature rich.
There are also other MP3 playing boards such as those from sparkfun but they do not include as many features. (Not that your application requires them)
For an application such as yours the wave shield is more appropriate, it is more designed to play sounds rather than the other boards that are designed for music.
Make your own choice there I suppose though. If it is going to be permenantly in this robot then the wave shield is probably the most appropriate but if you think you might only want it for that temporarily then I would recommend the rMP3 as there is a lot more you can do with it.
Do a bit more research on them and the other alternatives before you buy

- The Waveshield has a physical pot for volume, and can play loud directly on a HP. Does the rMP3 signal need an amplificator ? Is the volume easily controlled by software ?
I have not had a problem with volume but if you wanted to play loud sounds then it may need some amplication (so may the wave shield). This also depends on the speakers you use. I have some nice non-powered philips stereo speakers which are loud for saying they are not powered but if you just connect a speaker up to it then it might be too quiet.
- The Waveshield uses more pins, whereas the rMP3 is controlled through serial. What does this mean on the software side ?
Just like you said ;D
As far as I know, the rMP3 takes less processing on the arduino side as it has its own ATmega644 to take care of that. I have not used a wave shield though.
- The rMP3 appears more feature-rich, but as I'm not a code genius, I want something easy enough to use.
It is not tricky to use. Some of the fancy features can be a bit more tricky but there is this forum for help with things like that and there are examples you can use/look at to get an idea.
Mowcius