Oklahoma's offense is much more of a pro-style offense that absolutely requires an accurate passer who can make quick and correct decisions. He wouldn't be a good fit there, at least not as a quarterback.
Ohio State's spread-option offense can be modified so that it places a greater emphasis on a running QB's ability to make the read option. He could be successful there, if the OC is willing to change his approach from the current pass-happy offense led by Haskins.