My feeling is that in conversation they would usually be equivalent, but on a posted sign or in a public announcement, the second form would be more restrained and hence more polite. Putting the "only" closer to the beginning of the sentence slightly increases the degree of insistence involved, especially if the "only" is stressed. There is a slight degree of rawness and American-ness about "This will only happen after Sunday." If you were script-writing for a Texan rancher, you might use the former, but if you were writing lines for the butler in an Agatha Christie play, you might prefer the latter.

Mix and match:

"This will only happen after we leave Iraq."

"This will happen only after we leave Iraq."

Choices for each quote: Bush. Blair. Rumsfeld. The Queen.