I'd go so far to say that the computational power of an arduino would be quite a limit to voice recognition. [Bitvoicer](http://www.bitsophia.com/BitVoicer.aspx) for example uses the arduino to sample the speech but not to process and recognice it. It sends the stream to a more powerful system to do the recognition part. 

The Pi on the other hand is powerful enough to do all the processing itself as this [excellent answer](http://raspberrypi.stackexchange.com/a/10392/19949) points out.

If the voice commands to be distinguished are very rudimentary only (as your other [question](http://raspberrypi.stackexchange.com/q/32042/19949) suggests) it might be possible to get something done with the arduino. But I think that it will be bordering self mortification.