flare gun vs. shotgun
Depends on your playing style (ambush pyro vs support pyro), and very greatly on the map you're playing. Shotgun can be worth it just for sheer DPS when people are trying to run away, but its not very useful outside of medium range. There is no wrong choice here, but getting better at aiming with the flaregun is always a good thing.
backburner vs. flame thrower
Once again, situational. The Backburner is really only useful on key parts of certain maps, (the beginning area of Badwater, for example.) but isn't nearly as useless as most people will make it out to be. All in all, the flamethrower is still always going to be a better choice. The ability to reflect projectiles is absolutely lethal when used correctly, and the added ability to extinguish teammates just makes it all the more worthwhile. Theres nothing more painfull than watching a teammate burn to death in front of you because you choose the BB :\
C&D or Dead Ringer or normal cloak
All situational. In the hands of a good spy, the Dead Ringer is amazing, especially since the ammo buff. (minus the horrible decloaking noise.) I would still give it to the normal cloak though.
Ambassador or revolver (depends on accuracy?)
The Ambassador is TECHNICALLY still a superior weapon, as it can headshot-bodyshot any 125 hp class. Although, the revolver is still a bit more versatile, as most spys dont have that kind of pinpoint accuracy.
Kritzkrieg or normal medigun
They're balanced enough to were you wouldn't be able to say one is better than the other. Although, a Kritz cant save a dying medic, or patient, which is why I normally choose the medigun. One could argue that the shorter charge up time of the kritz is worth it, but given a good medic, Ubers don't take horribly long to charge to begin with.
A solider who is able to move and position himself without worry, and therefore make better shots, is more lethal than a solider with crit rocketsFaN or scattergun (more shots before reload or knockback?)
Six shots are better than two. Scattergun is currently the strongest close range weapon in the game, given that it can dish out upwards of 600 damage without reloading. The FaN begins to fall behind in DPS after about 2~3 seconds. Put in the hands of someone who can aim, (I'm looking at you, Jeed.) its definitely a better weapon.