Good grief, I looked it up and they had every animal under the sun in those rings. Yucky. It does still seem like the big cats were their main event tho.
No, they lacked any real sense of fun, bloodlust was had by all:sick
I think the obvious answer for the first would be ostrich, assuming the fighting conditions are equal and not favoring one or the other.
For the second, I've just gotta go lion. I think the stamina and agility of a lion would trump the brute strength of the bear. Lions routinely take down prey...