Like all answers relating to Cobras, the answer is, it all depends. A BB FE with aluminum heads, will come in very close weight-wise to a 289 with original cast iron heads. It's still an essentially mid-engine car, so you probably wouldn't notice the difference handling wise......except you'll have a harder time getting the BB to hook up.....
A well-built 390 could be an excellent "budget FE" choice, with gobs of low-end HP and torque, but it will still cost you to build it up right. How big is your bank account?
And, yeah, your rear end ratio would have to change
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