The big block version would definitely not be as much fun to drive as a small block. A friend of mine built a Sebring kit car. It looked like an Austin Healey but had a 5 liter Ford motor. Harry swapped out the fuel injection for a carb to increase the horsepower. and get rid of the computer. The 4 speed automatic would break the tires loose every time it shifted if you kept your foot in it. It handled surprisingly well considering all the weight up front.
A small block Cobra would be similar.
If the OP wants a fun driver, he already has one, and I suspect that is not his purpose in considering this car. If he wants to cruise and listen to those side pipes sing then this should work out just fine. It looks beautiful in the photo, and appearances would lead one to believe it is fairly well sorted. I would definitely try to have someone who is familiar with them look it over. There were a few different manufacturers of those fiberglass bodies, with some better than others. Do some research, if you haven't already. Check for visible clues of the build quality, but definitely have a qualified mechanic check it as well.
As someone who bought a 71 Volvo P1800 as a daily driver a number of years ago, I can appreciate the allure of a car you have always liked. I took a mechanic along with me who was an expert on the model. He approved it, I bought it, and it has worked out well. It appraised afterwards for about what I paid, so I did alright. There are a bunch of Cobras out there. Buy carefully, get your moneys worth, and enjoy the heck out of it.
And once again, be careful out there among the SUVs.