Remember, there's no rule that you have to use full blown .357 loads. In fact the .357 may be better if you want reduced flash, since the .357 can hold more powder and take higher pressures, you can load it up with a 'low flash' powder which may reduce velocity, but the extra case capacity and higher SAAMI pressure specs would allow a stronger charge to compensate. I'd rather the larger case with a milder load, than the smaller case being pushed to it's limits.
I'll take the .357... heavier gun helps control recoil, and you can still shoot .38's if you wish. But honestly a revolver would not be my first choice for 'home defense' I can imagine, at night, even a lowly .38spl will have a rather impressive flash from the cylinder/barrel gap. I'd rather not have what amounts to the equivalent of a flashbang going off, <2 feet from my face, every time I pull the trigger. Revolvers are cool, I love them, respect them. I just don't see them as a good choice for 'fighting' especially in modern times.
I'd be using a rifle classified as a pistol, in a rifle caliber like .300Blackout, or a semi auto pistol, personally but since that's not what this thread is about I'll take the .357 with some specialized loads. Either is adequate, neither would be my first choice.
BTW, I think a member on this forum had a negligent/accidental discharge of their .38 in their home. The bullet went into a leather jacked folded over a chair. Apparently, the bullet neither expanded nor did it exit the coat...