I prefer spring moving because it gives plants more time to adjust before winter. If you are able to scoop up roots relatively undisturbed, that will give the best chance for reduced adjustment no matter when it's done. As a general rule, moving things right after blooming gives them almost a whole year to adjust before you'll be hoping for more blooms, but I wouldn't wait to move a fall bloomer if I'm anxious to do it in the spring.
Ideally, I try to move plants when cloudy conditions are expected so plants don't have beating sun or too much heat during the first few days after a move. But if that's not possible, using a table or chair to create some temporary shade can help, and checking in the mornings to make sure the soil is not too dry.
