Inquiring minds want to know.
front than
I think smaller wheels at the front make for more effective and easier steering.
Just an educated guess:
If they were any larger, I think they’d hit the side of the body. You’d have to extend the wheelbase or width to prevent this, which would mean increasing the overall size of the coach. Small wheels seem to be a good compromise.
The rear weels don’t swivel (steer), so they can be made larger without hitting anything. And larger wheels provide a smoother ride.
Apart from the sensible answers above, the hero would have a more difficult job clambering onto the stagecoach to restrain the runaway horses and rescue the heroine.
I am with aldiboronti on this one. I am not quite old enough to have actually driven a stage coach, but having worked on a few hotrods, I know the smaller wheels are easier to turn. Wide tires also raise heck with steering issues. No power steering on stage coaches. Hopefully not needed on a hotrod. (unwanted weight). So the steering tires stay narrow and small.
This is a little hard to explain without detailed pictures. However examine the wagon with two people in the picture. The whole front axle assemply including the shafts and wheels is one unit. This means that below the wagon box there is a fairly long, or high, assembly that functions as a bearing, which needs occasional grease, and pivot so so that the front axle assembly can turn.
This places the front axle a particular distance from the ground with a given size of wheel. Now look at the rear axle. There is no bearing and pivot assembly there so the axle is higher off the ground than is the front and this requires bigger wheels in the rear. If the wagon box is to be level either the rear wheels must be bigger or you need to put a dummy bearing between the rear axle and the bottom of the box.
And it keeps stuff from sliding out the back. 