It's more difficult to mount a workpiece on two round pins than on a round and a diamond. Be careful - the orientation of the diamond pin is important to the locational integrity of the fixture. I recommend you find a good, illustrated book.
A line running through the wide points of a diamond pin are always located perpendicular to a line running through the axis' of the two locator holes. No books on theory required, just some "oh yeah - I get it!" common sense. Hope that helps!
A diamond pin is meant to handle the variation (tolerance) of the distance between the two locating holes.
Two round locating holes with diameters closely sized to the locating holes diameters may not always accept the allowable distance variation between them.
Remember...
"If you don't use your head,
your going to have to use your feet."
All are good posts. One other way to look at it. a Dimond pin allows you to line up two holes while ignoring the error found in the pitch between the two holes.
Typically this is called a two-way locator as it locates the part in the up-down or left-right (only two of four ways) direction. This is opposed to a round pin which is a four way locator. You can't move the hole in the left-right and up-down directions.
This is commonly used to create your part alignment on the B-C datum line (In CMM speak this creates your line.) The round pin is your four-way locator which defines the origin of the part (Your origin or point from which all other points are relative). The diamond allows you to properly align one of the axis of your co-ordinate system through the center of the hole without making the part extremely difficult to load onto the fixture.
You are all close but the real problem is the true position of the holes, no two holes are exactly the same distanct apart. The round pin locates the primary hole in both axes and the diamond pin locates the perpindicular axes of the secondary hole alowing for some devation in the location of the two holes. The diamond pins long dimension needs to be perpendicular to a line through the two holes.