There's no handling or ride comparison between the current LX platform and the E-bodies of the 70's.
While the solid (live) axle of the E-body Challengers is better suited for the strip (acknowledged by use of the live axle used in the black concept car for the dragway), the ride, handling/cornering, body roll, turning radius and squat from a dead start under hard acceleration in an LX car is like comparing champagne to Boone's Farm. With the LY having the same track as the LX but a slightly shorter wheel base, the LY Challenger should turn a bit better, be a hair lighter, but hide bumps in the road just a little less. I'll assume that since it's a two-door, it will be equipped with a bit firmer/sportier suspension so you'll have more road feel through the chassis and steering than the current LX cars, but still enjoy the better overall ride and traction of four wheel independent suspension.

Engineers are much more saavy now than they were 35 years ago. The competition is much more formidable and engineers know that the whole package has to feel right to compete. It used to be that "the big three" were after bragging rights as to who's car was the fastest/baddest/most desired on the street - who could stuff the most HP under the hood for straight-line acceleration. Now, "the big three" are "number three through five" in the US. It was a hard lesson (still being learned) that the Japanese car makers brought over-seas with them and basically, "took the US automakers to school". Finally, GM, Ford and Chrysler are learning that they have to balance HP, cornering, fuel economy, reliability, appearance, safety and functionality to sell cars and stay in business. Now, big brakes go on a big car, the gearing has to match the wheel size for an optimum balance between performance and reliability, and it takes much slicker marketing than dumping a scantily clad girl in front of their car in a TV ad with a catchy jingle to sell cars.
Did anyone know what the Corvair's crash test rating was when that car was on the market?
Did the Monaco come with front and side-curtain air-bags?
Sorry, I digress.....
The point I was getting at is that EVERY new car, and nearly every new "light truck" and SUV handles better than the cars Detriot was rolling out in the early to mid 70's.
Take a trip to your Dodge dealership, take an SRT8 Charger for a test-drive, and lie to the salesman and tell him the ride is too harsh - you're not interested. Then go home, drooling and knowing that the Challenger will be better than that! I don't think you're gonna be disappointed.

Getting myself all worked up..........I think I messed my pants.