Factory mopars were WAAAAAY undersprung from the factory in the front, the torsion bar spring rates are pretty low. My suggestion would be that if you're planning to do any significant amount of street driving at all you should upgrade the torsion bars, regardless of any engine swaps. As Joe mentioned, drag racing is a whole different story. Keep in mind, when these cars were stock from the factory, their performance in acceleration,handling and braking was fairly well matched with all the other cars on the road. Now, although the acceleration may keep up with a V8, handling and braking does not, which means the majority of cars on the road will out-handle and out-brake a stock equipped A-body. That's probably not the place you want to be if you're driving your A-body a lot. You'll want to keep pace with everyone else, and you'll sure as hell want to stop when they do (suspension effects this too, not just the brakes).
The 1" bars from Just Suspension (or whichever vendor you prefer) are a good upgrade. The car will handle MUCH better, even without sway bars or other changes, and the ride quality will still be fine, even for a daily driver. Obviously better shocks and sway bars would improve things more.
Surprisingly enough, the specs that I've seen on the /6's and 273-340's is that the engine weight is pretty similar, to nearly identical, depending on who you get your info from. I've seen the slant 6's listed from 470 to 525 lbs and the 273-340's at ~525 lbs. 360's are little heavier, but only by about 25-30 lbs (550-555, depending on who you ask). So if you've been replacing cast iron with aluminum, the engine weight change might be pretty negligible.
But the change in horsepower will not be. Faster acceleration means more weight transfer. More power also means you'll be able to accelerate rapidly in places you couldn't before, like say, in corners. Or in between stop lights, which might also involve stopping faster from a higher speed than if you were pushing a /6, which means more dive on the front end if you're running soft torsion bars. Especially going from a /6 to a 390 with alloy heads, you'll be going from 100-150 hp to likely over 400!!! You need to upgrade the ENTIRE car, not just the engine. All that horsepower won't do you any good if you can't get it to the ground, or worse, control the car when you do put the power down.
