<p>I was wondering if anyone that has experience in both this stuff can shed some light on the <em>significant</em> difference between the two if any?</p>

<p>Any specific strength of each that makes it suitable for any specific case?</p>

I found SimpleTest was even easier than PHPUnit to set up. Just extract it and you are good to go. A benefit of this is if you are working at more than one machine, since you can store the whole testing framework the same way as your source code, and thereby know that you are using the same framework code. Especially if you modify it in any way.
So, I would say that a strength of SimpleTest is that it is very light weight and portable.
SimpleTest also ships with a very simple HTML GUI, which is quite easy to extend if you want to. As far as I know, PHPUnit does not include a HTML GUI, but there are GUI:s available to download, such as
Cool
.