The first thing I would suggest would be to split up the actual comparison so that it's a bit more readable (I've also taken out the ToString() - is that needed?):
else {
object originalProperty = sourceType.GetProperty(pi.Name).GetValue(this, null);
object comparisonProperty = destinationType.GetProperty(pi.Name).GetValue(comparisonObject, null);
if (originalProperty != comparisonProperty)
return false;
The next suggestion would be to minimise the use of reflection as much as possible - it's really slow. I mean, really slow. If you are going to do this, I would suggest caching the property references. I'm not intimately familiar with the Reflection API, so if this is a bit off, just adjust to make it compile:
// elsewhere
Dictionary
However, I have to say that I agree with the other posters. This smells lazy and inefficient. You should be implementing IComparable instead :-).