This one's a little tougher, but not for good reasons. I'll note that I didn't like most of these songs when they were released but (like a lot of 80s pop) have grown to like to some degree.
Category 1: Billie Jean is ok for an MJ song. Good melody and beat. Every Breath is just ok. Very overplayed and, IMO, overrated. Can't stand anything Springsteen.
Category 2: The reed players in my daughter's high school marching band play Careless Whisper as a joke. 'Nuff said. Not sure I can distinguish the INXS song from a couple others (didn't they also have one called The Kick Inside?), but I've never heard anything by INXS that I liked. Don't know the Moody Blues song.
Category 3: Borderline is a relatively weak Madonna song. These Dreams is one of my favorite Heart songs and the best song in this poll. While I don't hate Let's Dance like I used to, neither do I love it.
Category 4: The best thing I can say about 1999 is that it's better than most stuff that Prince did. You Might Think isn't very good and gets marked down for the video that seemed to run on an endless loop on MTV. Uptown Girl is cool, but not great.
Category 5: In the Air Tonight is pretty good. Shout is a great 80s pop song. Second best song in this poll. The Elton John song is ok. Good melody. Nothing great.
So this comes down to 3 and 5, and I think 5 gets the nod. Might be a different result with a different Madonna song.