Ultimately, its a numbers game. If you can buy an old duplex for $15K and put $25K into it, and get the same rent as the $100K duplex, there's no question. Buy the old one.
Compare the total price - purchase plus rehab - to the rent. The better that ratio, the better the deal.
You do have to consider demand. If there is a lot of demand for nicer units and none for lower quality units, then you might want to go with the better ones.
And, you're right about the tenant base and the neighborhood. You don't want to be in a war zone where you're only going to get bad tenants, and you property is going to be at risk. On the other hand, you don't want to be in a swanky area of mostly home owners where prices and rents are badly out of whack.
A quick and dirty calculation is to assume the expenses will be 50% of the rents. Whats left is your NOI. Then figure your P&I payment assuming 100% financing at investor terms on the purchase price plus rehab expenses. Subtract that from the NOI to get cash flow. Some landlords, especially in OH where there are limited growth prospects, want $100/unit in cash flow. Read in the Rental Property Forum for some background on the "50% rule".
If you can post details of your prospective deals, we can give a better analysis.
I didn't look at a map, but I assume Sadieville is close enough to Cincinnati and Columbus to drive there. You should go do some driving and get an idea of the areas you're considering.