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I think it is definitely true that a lot of people leave their 'big gun' at home because they think they can judge when they are going to find trouble.
I've found out several times that the truth is that the REAL world is not at all like the movies - you can't tell when a bad thing is about to happen, just because the character goes into an unusually bad neighborhood, or because the 'scary music' starts...!
I've been in some terribly dangerous neighborhoods at terrible times of day, and. . . . nothing happened.
I've been in some very 'safe' neighborhoods during broad daylight, and. . . . violence happened.
So I don't 'triage' what gun I carry by just carrying something tiny/token "unless I'm going to be in a bad neighborhood". When it comes to firearms used for protection, overall size is pretty well proportional to capability, so that is really the determining factor - as it affects comfort and concealment. I pretty much learned to ignore 'comfort', so never have minded carrying a 7" Revolver or 5" Semiauto, and live in a place where 'concealment' is mostly something we do just to be polite, but isn't all that vital.
I guess my scheme of things is to consider my home a Jeff Cooper 'white' zone - super low risk (due to type and position of dogs, gates, lights, motion detectors, doors, locks, etc), but ALSO the most precious place - so I will indeed be armed with whatever is the largest most practical defensive firearm given my level of activity. So...what would I exactly 'upgrade' to when going elsewhere...? I STILL carry the largest practical CCW firearm for a given activity, and the only things that would make a full-size 'duty' gun an issue would be not wearing a belt or going swimming. I'm to old to not wear a belt (I've lost my girly thin waist), and I hate swimming (although I have clipped my NAA 22 WMR Mini-Pug to the inside pocket of swim trunks - 'just because I could' - a couple times

)
So realistically I'm likely to have the same sort of firearm on my person wherever I go. The only difference might be which one - if I'm pouring a concrete patio or doing other grimy abrasive work, it will more likely be one of my Glocks or my AMT 1911 clone than my nicely-finished Para Ordnance or Ruger or Colt or Beretta or even the Ruger RXM Glock clone, just because I don't want to unnecessarily risk damaging one of the harder-to-replace or more-cherished guns.
I guess there is a 'third' situation other than home-versus-away, and that would be if I were to go into a clearly-dangerous neighborhood in clearly-dangerous times of day. Then I'd still probably be carrying what I'm familiar with, actually, although my STRONG inclination would be to not go there in the first place. If I did have to though, I think the MAIN difference wouldn't be in the equipment on my person, but moreso my level of vigilance.
Back to the "UNDERCOVER" topic though - it reminded me of the 'bathtub' scene in the Good the Bad and the Ugly -
https://www.youtube.com/watch?v=Nk2-rfTbl-w
I do know several folks who specifically have a 'stash-gun' in their bathroom stored in a zip-lock bag or similar - one was a woman who got attacked in her bathroom in the past - if it happens to her ever again, the rapist is in for a surprise.