Again, two highly similar weapons that have enough minor differences to actually matter in gameplay.
http://fallout.wikia.com/wiki/Lucky
-Cheaper and easier to repair (cheap at NPCs and fully repaired .357 magnum revolvers are BEYOND cheap)
-Possibly the most common type of ammo in the game (.357 is found from beginning to end, and in heavy supply in both Dead Money and Old World Blues)
-Slightly lower AP cost (17 vs. 19)
-One extra bullet in the chamber (6 vs 5)
-Reload sequence can be interrupted prematurely, though reloading a full clip takes longer (POTENTIALLY reloads faster if only a bullet or two more is needed, otherwise reloads slower.)
-Lower spread (hand loader ammo makes this point practically moot, with a spread of .24 vs. that of .325)
-Slightly higher DPH with hand loader ammo (x1.25 multiplier vs. x1.15, alongside -3 DT vs. -0)
http://fallout.wikia.com/wiki/That_Gun
-Faster reload speed (USUALLY faster, though Lucky's ability to interrupt prematurely can be an advantage when only 1-3 more shots are needed to finish a fight)
-Higher DPS (basically a moot point once Hand Loader ammo is factored in)
-More ammo diversity (the only sidearm that can use AP rounds)
-Ammo is still found in large quantities at vendors, even if the ammo type is less commonly found in the world
-Ammo type weighs less (.026 vs. .035. Potentially moot since That Gun weighs twice as much as Lucky, so this only shines when you carry an excess of 300 rounds or 600 with Pack Rat, otherwise Lucky is less cumbersome)
Both of these guns benefit from Cowboy, both of these guns have high crit rate of x2.5. One should note that a low agility character will IMMEDIATELY shy away from Lucky and find That Gun superior based on reload speed alone, but this question mostly focuses on how the two compare with mid to high agility characters.
Again, I would be very tempted to pick That Gun simply for the sake of ammo diversity, but knowing that these are sidearms and thus more likely to function and be used as secondary weapons and NOT as primary (since let's face it, many weapons are undeniably better than these two on the damage fronts), experience tells me Lucky is the superior, simply because of the ease and low cost of repairing it alongside the likelihood of simply finding more ammo for it during your travels. I can also speak from experience that as petty as that extra bullet in the chamber or the ability to interrupt the reload sequence may seem, it has -literally- saved my life vs. nightstalker swarms, where having one less bullet or having to wait for a full reload sequence would've simply been the difference between life and death. Still, while this would definitely put Lucky as having an advantage vs. enemy swarms (Nightstalkers, Cazadors) simply for having better ammo management, one cannot deny that if you WERE to choose one of these guns as your main weapon or if you WERE to need to fall back on your sidearm for high DT enemies for some reason, That Gun has an undeniable all-around advantage simply thanks to it's ability to use AP rounds, giving it a 12 damage per shot advantage over Lucky when it comes to fighting Deathclaws or other high-DT opponents. One should also note however that for low-DT opponents, Lucky actually ends up with a minor advantage when Hand Loader ammo is involved, both for having a higher bonus to the damage multiplier and for shaving off 3 DT with basic rounds, meaning That Gun is immediately losing out on 3 damage points that Lucky isn't.
But of course, I'd like to hear your opinions on the matter and I'd like to hear what the community concensus is.