It depends on how you achieved Diamond.
If it was a status match, and you only have only stayed 1 or 2 nights, or none as of yet, you will not be able to get a status match with another chain.

Usually, the other competitor will ask you to fax in a statement of stays, as evidence.

If however, you got diamond by staying the required nights with Hyatt, you should get a status match with virtually every other competitor.

Most forums have a status match thread with plenty of detail in to read.