The auras given by the Soldier's banner buffs have these color schemes:
- RED: golden-yellow glow
- BLU: cyan-aquamarine glow
Whereas the auras given by the Medicating Melody or Quick-Fix ÜberCharge are standard red and blue in color respectively.
A player being buffed by the Buff Banner will have a weapon glowing the same color as the aura, so a RED player for example will have both a golden-yellow aura and a golden-yellow weapon. A player being buffed by the other banners won't have a glowing weapon.
Telling a Battalion's Backup buff from a Concheror buff is more difficult: if you're looking at the Soldier who deployed the banner, he'll be carrying a different flag; see Retrosaur's answer for what the banners look like. However, if he isn't visible, you won't be able to tell which of the two buffs his teammates have received unless you heard the horn, or until you engage them in battle.
The difference between a Medicating Melody and a Quick-Fix ÜberCharge is that the latter will also shower the Medic and his patient with sprinkling healing crosses, not to mention the presence of a healing beam.
From what I've observed, all auras pulsate at the same frequency.