Lets weigh the different options:
- Revolver / Big Kill - Standard damage. Kills lower HP classes in 3-4 non-crit hits.
- Ambassador - Lower damage shots, slower firing rate, no random critical hits. Headshots do 102 damage if you haven't fired recently... you can tell because the firing reticule in the center of the screen will be at its smallest size. Kills lower HP classes in 2 hits if one is a headshot, otherwise 4-5 hits.
- L'Etranger - Lower damage shots, recharges cloak on hit. Kills lower HP classes in 4-5 non-crit hits. Extremely useful when being used with the Dead Ringer... less so, but still somewhat useful with the Invisibility Watch or Cloak and Dagger. Also part of the Saharan Spy set, in case you want the silent decloak set bonus.
- Enforcer - Higher damage shots, cloaking takes half a second longer. Kills lower HP classes in 2-3 non-crit hits. Extremely useful with the Dead Ringer, where the downside doesn't apply.
- Diamondback - Lower damage shots, no random critical hits, gets guaranteed critical hits when your sappers destroy buildings. Kills lower HP classes in 4-5 non-crit hits or 2 crit hits. Unless you're fighting mini-sentry Engineers, this gun is largely inferior to all the others.
These days, I tend to flip between using the Enforcer with the standard Knife/Dead Ringer and the L'Etranger with Your Eternal Reward with any cloaking device (and Saharan Spy set). Occasionally, I'll use the L'Etranger with the DR and standard Knife or the Saharan Spy set with the Dead Ringer.
In terms of pure damage, if you have time to aim, the Ambassador is your best bet. If you can't, the Enforcer is. If you tend to run out of cloak a lot, the L'Etranger can help, but remember that you break disguise when you shoot enemies with it.
In my personal experience, the L'Etranger seems to miss more than the other guns. All revolvers shoot straight down the reticule for the first shot, but somewhat randomly for successive shots until they cool down. This is much easier to tell on the Ambassador, as the cooldown is identical to the headshot cooldown.
Having said that, if you have auto-reload on, the reload animation takes slightly longer than cooldown, so letting it autoreload and complete the animation is another good way of telling if the cooldown is done.