Less escorts, more champions.
It’s most often a chain, escort, kill pirates, then champ. Though not all the time. Anytime I came across a tower I just completed the chain of events before I moved on. I was able to complete that achievement by day 2, about 15 balloons into the 30.
The Queen’s Champs always spawn in the exact same place on all maps. If you know where they are, and you know which ones you still need to kill, you can go see which one is on standby. Then you can camp there and wait for someone else to activate them, or complete the quest chains to activate them yourself.
In GW2, Trading Post plays you!
Actually, none of them are more likely than the others. It always goes in the order of excort → kill pirates → champion fight, then repeats (it doesn’t do it randomly). They all happen 1/3 of the time, though I suspect you might find the escort one unfinished more often because people are less likely to want to try to do it.