If you're just going to be using it on the street, I don't think it'd be worth changing to the Dana 60. The change in the front/rear bias will be pretty minimal, and knowing how to handle your car is more important than a perfect 50/50 weight balance.
Also, its a lot easier to change gearing with an 8 3/4. For racing, this is important since it allows you to tailor your gear ratio's to the specific track you're at. Gear changes in the Dana 60 aren't nearly as quick and easy.
How is the 340 set up? I'd be more inclined to switch to an aluminum intake, heads, etc to lighten the front, rather than making the rear heavier.
Agreed on knowing how to handle it is more important, ultimately it's about the nut behind the steering wheel. However, I think better handling can be had than what I have now, so why not try to achieve it?
Gear changes isn't a concern. I pick a gear, and I stick with it. No serious track or strip use for the Chally. Fun on the street is everything (With some allowance to highway use, i.e. not too low gears). Of course while pretending very hard to be a responsible adult.
The 340 got a aluminium intake, won't do much about the engine until I decide whether to go for SB or 3G Hemi.
A big factor is what my friend and closest e-body owner widing'cuda does enginewise, it's important to top him. He's been top dog too long now.
He's strongly considering a new engine now. Maybe I'll let him have a year to enjoy it before I go
on him. This is of course only because I'm a kind person, nothing to do with me needing more time to save money for upgrades. No Sir, not at all. *Cough*
the extra weight of the Dana on the tires does help traction 
Burnouts are cool, but traction is the action.
Well, gasoline weighs approximately 6 pounds per gallon. If an E body tank is approximately 16 gallons, then half a tank of gas is just under 50 pounds of weight.
I do understand that the weights themselves are comparable, the matter was of the position of the weight.
I was only wondering about any noteworthy handling downside to have the added weight under the springs, meaning more mass for the springs to handle, skewing the sprung to unsprung weight ratio.
I.e. being more unsprung weight to work against the same sprung weight.
But now I get the impression that handlingwise it doesn't matter whether the few extra pounds in this specific example are on the sprung weight or the unsprung weight. I guess that as long as the road surface isn't full of bumpy bits, it should be fine. If the road is full of potholes, I won't be doing any spirited driving anyway. So I think the preparedness for future shenanigans, better traction, tiny bit better balancing, and last but not least cooler look might be worth the effort later since the damping cost isn't very high. Besides, I don't smoke, hardly ever drink, no wife or children, so I have to spend money on something.
If you are going to buy a Dana 60 from someone who sets them up in any configuration you want this would be a good time to consider a different length axle to suit a desired wheel offset. Also, you can take advantage of using the 'big Ford' housing ends for a better bearings than the Mopar 'green' bearings.
Strange would have done all of this on my order but I neglected to plan for the future and now I am narrowing my new S-60. If you are building it yourself you may also want to consider a b-body housing.
That's good advice. I'll certainly have that in mind if I go for a Dana 60.
With all that said, I'm only exploring an idea now. The priority is to sort out some rust and other body issues next year.
