Kirby answered my call and has been releasing some excellent data from 3++ Con that has helped demystify some of the assumptions people have about the game. Please take a moment to read over his breakdown of going first/second and then come back.
So going second doesn't have a big advantage over going first. But going first is clearly slightly disadvantaged, even in non-objective missions? Why? Much like in College Football overtime, whoever goes on offense second knows exactly what they have to do. If the first team on offense kicks a field goal, the second team knows they have to kick a field goal at least, and if they get a touchdown they win. Their path to victory is defined. The team who goes first has to simply do "their best" and hope it works out. If you're going second and you know it's the last turn in WH40K you know exactly what you need to accomplish to win. You still have to actually execute that plan, which is why there isn't a huge advantage to it, but an advantage nonetheless.
Also curious, the worse your record the more advantage there was in going first. Kirby offers some explanations of that, but its quite possible that players of a lower playskill caliber are too linear in their thinking and forward planning to take advantage of the benefit of second turn advanced planning. Additionally, when looking at just the winningest players' brackets, going second has a rather clear advantage.
The sample size of one tournament is small enough to make us hesistant to draw any firm conclusions, and hopefully NOVA and Adepticon do a similar breakdown this year. But I am pretty sure that until I see data suggesting otherwise, I am going to take the second turn as often as I can.