When I set notifications to show via Growl, the Display Notification action has an Options button which allows me to choose whether or not the notification stays on screen until manually dismissed.
When I set notifications to display via Notification Center, the options button vanishes and I can't select this. Notifications all vanish automatically, usually before they're read.
I find having both Growl and Notification Center throwing notifications at once a bit annoying, and would rather put everything through Notification Center. I've definitely seen other apps display persistent notifications (though I wish OmniFocus was one of them!) so it must be possible — is there a reason Hazel doesn't support this?
(As an aside, with Hazel 3.3.5, if you change the notification type from Growl to Notification Center, all actions still show as "Display Growl Notification" with the Options button until the Hazel preference pane is closed. On reopening, the option correctly shows as a Notification Center notification once more :)