Since both the latest versions of WMV and MP4 can be pretty close in
quality, at least from what I have found (and read about), that means the WMV
one was compressed considerably more than the MP4. In which case, you
should see more artifacts in it, unless the bitrate was high enough in
either case so as to not see them. That required bitrate depends greatly
on the video size. For example, a 480x360 will require a lot higher bitrate
than a 320x240 one.
When the bitrate becomes too low, you will start noticing blocking artifacts,
similar to what one can see on the JPEG comparison page mentioned here by
Paul in regards to the recent photo compression discussions. And then loss
of high frequency detail. Etc.
But if you can readily get the WMV ones, and you are happy with the resultant
video quality (which depends on the quality settings the conversion is
using), that could be the easiest way to go. :-)