At issue is the ly, which some find unnecessary (and somewhat snooty). Many sticklers do not accept importantly in the two sentences that follow: I left my bed and, more importantly, I left the house. Most importantly, Churchill was a statesman. Critics of those sentences would prefer "more important" (what is more important, I left the house) and "most important" (what is most important, Churchill was a statesman).
Other experts declare the phrases acceptable with or without ly. But since brevity is a virtue, why not drop the ly and save yourself a superfluous syllable?