Arduino is much more capable of doing things then the lego mindstorms.
So if you want to program a robot arduino can do the job very well, but it depends also on yourself, i mean you need to do a lot of reading and experimenting to get familiar with the whole concept.
And shure there are extensions which you can use to operate your system, but that needs to be programmed as well.
I suggest you find a board and do some experiments first to start building a robot, or buy a robot thats build on a arduino controller.
I myself have a aar-04 from Arexx.com the cell them at Conrad in NL,DE and UK, it works fine for me to get familiar with the code and functions you can choose and use.