You also need to understand that there is a Southern culture, and you are a Yankee. I speak with experience. Non-OSU daughter went south to an SEC school. She had to get adjusted to it. Are you interested in joining a fraternity? Alabama is a very big Greek school. When you visit, you might want to really pay attention to the vibes you feel while there. Do they feel good, or do you want to get the heck out of there quickly?
I get the dollars aspect, it is a huge issue these days. You really don't want to saddle yourself or parents with too much debt. And if you really want to get out of Ohio and go someplace, then Alabama might be a better fit for you. Now, that being said, do you hope to come back to Ohio after graduation? If so, an Alabama degree might not get you in as many doors as an OSU degree will. Not to mention, you will not make the same connections being out of state for 4 years. And these days, connections and internships often give you a leg up. But if you are flexible as to where you go post graduation, that point might be moot.
Have you called the OSU scholarship office? Let them know that you have a full ride to Alabama, they might up your scholarship $$. It does happen.
Good luck! It is a big decision.