Here is my vote:
Saul's Story: My personal No. 1
It is great fun to play with Thommis, Hablion and especially Dorian, he just looks too funny.
The hide and sneak part was quite nice, I also noticed that the area where this takes place is in the green jungle area between the Verdant Cascades and Kryta. This could mean the Charr tried to invade over the Norn territory and not through the more southern Stone Summit part of the Shiverpeaks near Ascalon.
Then you destroy 4 Charr Warbands. Quite cool to slaughter tons of low level foes, but it quickly gets old. They can hardly harm you after all, and you have a 7 second recharge - 3.5 with the Mantra of Inscription - 80 Holy AoE damage nuke signet. This is a general problem of all 4 missions, hordes of low level foes versus incredibly powerful player skills.
The last boss killed me, the only time I died while playing the BMP, seems to be the hardest of all 4 missions to me because of the final encounter. Which does not mean much.
The cinematics were very cool, how Saul realized his mistake and his false gods was nicely told.
Togo's Story: Rank 2
The cinematics were really nice. Especially for the assassin guy. Not so cool were the skill selections. But it was at least more challenging than Saul's mission in general, the final boss was not really strong though.
The big gripe is the 8. skill on the bar. Basically, wait for it to recharge, wait till they kill Talon and then wipe the floor with all of them. Boom. Wonderful, makes Saul's uber signet of mass carnage look like a tactical weapon. I am not sure if this should really be an example for GW2 missions.
Gwen's Story: Rank 3
Not much fighting, and often I ran around rather helpless having no idea where to go. Also, having "FLEE" and "THROW ROCK" as skills for a PvE Mesmer made me chuckle.
But killing the Devourer by destroying the pillar and playing hide and seek had some appeal. Better than killing another horde of 1.000 lowlevel Charr that do not stand a chance. Not as much replay value as the other missions though.
Gwen running around in this white prisoner garb is also a sight to behold. No, not because Pedobear agrees but because it gives the whole thing a dramatic touch.

Turai's Story: Rank 4
The Battle of Jahai is depicted from a distance, I could not really immerse myself in it. So I fought the rear guard. The ultimately BEST thing about this mission is that you get a free r9 15-22 Turai Ossa Sword, basically an Eternal Blade that is not yet Eternal. I also like the shield skin very much, I might replace my gloom shields with them.
Turai seems to be a half-Jotun, he giant stomps the little undead guys and well... pure carnage. He reminds me of William Wallace, who is also a giant, shoots lightning from his eyes and whose farts knock down people, too. He walks a bit sluggish and slow for his size, the animation was not right imo.
At least he has to fight a little bit more because he does not have the same uber-nukes as Togo and Saul.
The final cutscene was very cool, though the battle with Palawa was not very exciting.
Discoveries: Very nice idea, did only Gwen's so far (finding Hideouts). A bit like the hidden Prophecies bonus missions.
Weapon Skins: THE reason for the BMP
An unlimited source of some of the better skins ingame. I really love the skins, but I am not sure if this is a good thing... what do you think? Turai's Sword also makes a great hero weapon.
General comment: The cinematics are great. As are the rewards. My gripe with the rewards is that you can get limitless numbers of these items, even if they are customized. Endgame items are limited to the one you get on your first completion, too.
Maybe one should be given the option to exchange the item for another one from the same collector in case you made a mistake, the endless supply of great skins is just too good. Now one must be really a snob to buy rare item skins, because the BMP provides quite a lot of supreme skin styles. As I mentioned above, I will replace all my Gloom Shields with Undead Shields.
The gameplay was storydriven (rather good stories, IMO), fun and diverse. The thing I did not like was the skills given to the player and the extreme mindlessness and low level and sheer masses of enemy mobs.
I do not expect smart enemies. But they should fight back a bit harder and require some more thought than in the BMP. This should not be a gameplay design example for GW2 -> if this is the case, I am gone. UBER HERO player vs tons of level 12 foes? Not really that cool, I say go back to Prophecies, 4-6 man parties vs a bit larger enemy mobs like in the Shiverpeaks, with higher or equal level and some more challenge. I.e. kill the healer, then the rest. This is all gone in the BMP, the mobs lack diversity. Even if this is for story reasons, it is bad.
The dozen of canthan guards charging you is great the first time you do it, after that it is really silly. Use the Togo Nuke (tm) and you are done.
The story driven parts of the mission where you had to do something else besides killing were great. I think Togo's mission would be much better if you did not have the nuke and stupid enemy numbers. So yay for the fun mission objectives, nay for the actual fighting!
My Verdict:
The reason you are playing this is to experience the story and the cinematics. After that, to get your favorite skin weapons/shields. It is really just a "bonus" experience. But more of this in a game with more content is for sure nice.
What is a bit sad is that the tactical game is lacking. PvE was always easy, but now it gets dumbed down totally, and hopefully this is only the case in this BMP, and not a hint of how GW2 will be. The cinematic cutscenes rock, the mission objectives rock, but the actual fighting needs to become better and not dumber, too.