Its an interesting question, there are so many aspects to it depending on the type of vehicle, two wheel drive or four wheel drive, type of centre differential, and where and on what surface its driven especially with a locked centre diff.
One thing to think about is that most if not all radials these days have a steel belt to give vastly improved sideways stability to the tire. Now think about that for a moment. The steel belt cannot stretch or change length under high or low air pressure. The tire circumference does not change. It does look awfully flat at the bottom with less air, but the rolling circumference does not and cannot actually change.
On a low speed 4WD tractor I would think fitting the same sizes as the recommended factory originals would be all you need to worry about.
On a high speed road car, radials and cross plies have completely different handling characteristics.
Definitely the same type on the same axle, but you can mix fronts and rears, but its probably not a very good idea.
If you must mix front to rear, then always the radials must go on the back no matter which wheels are the driven wheels.
The reason for that is that at the limit of adhesion the radials will always grip better and hang on for longer assuming good tread and a dry road. The cross plies roll onto one shoulder and then let go suddenly.
If it breaks loose at the front you go off the road facing forwards, and may still have some limited control (understeer). You crap your pants, but at least you and the car probably survive the experience.
If it lets go at the back (oversteer) the car will spin and an inexperienced driver will immediately become disoriented traveling sideways or backwards off the road with absolutely no control at all.
A controlled crash is always better than an uncontrolled crash.
You might just be able to avoid the steel pole or concrete wall at the very last moment if you are still traveling forwards and can see ahead with some minimal control of direction.