Without a doubt the .223 would be cheaper, and do quite well for yotes. I have a Handi with an Ultra 223 barrel on it and it shoots very well.
I think the difference between the Ultra and the plain Jane Handi would be the stock. If you look at the frames of the two side by side they look the same.
But the .243 would be an excellent muti-purpose round, and the coyote rounds would reach out further.