A lot depends on your stroller, we have a Maclaren one that folds up quite small, so it's not too big of a hassle. Generally when you get to security, you have to take your LO out of the stroller, fold it up, put it through the metal detector, and carry your LO on. Like the PP I thought it was great to have though just because I could hang my bag off of it. I just did a flight a few weeks ago with my then 18mo where I had her in the stroller, hung the diaper bag and my purse off the stroller, and had to drag the car seat behind me (and was 35 weeks PG, what an experience!).
Anyway, I think a lot depends on how active your LO is as well. If she's a more active sort, you might be better off with the stroller and if she's content to sit, the Bjorn might be better.
As for boarding, it depends on whether or not you've got a seat for her. If she's got a seat, I would board early to get her situated. I had to strap DD's car seat into her seat on our last flight and needed all the time I could get to get her settled and in the seat. If she's sitting on your lap I would board at the very end since you don't really need the time then and the less time spent sitting (esp on such a long flight), the better.
DD's been on four round trip flights already (though none longer than 4 hours) so let me know if you think of any other questions.