I have a similarly sized car, tubbed with 16" wide tires on the rear. I have 225 60 15 tires on the front. I have had it for 20 years, and have driven it many thousands of miles. 454, turbo 350, 9", 3.50 gear
For the most part you don't feel a difference, but... On certain roads with heavy truck traffic, there are ruts worn in the roads that you don;t notice with standard tires. With a tubbed car, the tires tend to run on the inside edges of the ruts, this tends to throw the rear of the car from side to side. It feels like a flat tire, very disconcerting at first.
Body roll does increase some. but not as dramatically as you would think.
In most cases the rear end/tire combination is heavier than stock, even with aluminum wheels. This increases the unsprung weight, making the body react more to bumps than it did before. On certain roads, with prominent expansion joints, at a particular speed, the rear of the car can start bouncing rhythmically. Increasing or decreasing speed cures this, just something to watch for.
You have to be very careful on wet roads, the rear tires hydroplane very easily. I had this happen to me, on a wet road, after a rain storm, at 25 mph.
Unfortunately I hit a tree. $3,500 for repairs, it could have been worse.
The biggest difference is braking, the front tires will almost always lock before the rears on hard braking, no surprise. Front tires sliding give very little directional control, also no surprise. It's the nature of the beast, so you have to take that into account. Putting as wide a tire that you can reasonably fit on the front helps this a lot, no 4" tires in front, no matter how cool it looks.