I've had both for many years, and I'll tell you one thing ... go for the credit card.
I can never seem to pay off my overdraft, but I've paid off my credit cards and re-used them multiple times, while my overdraft is just happily sitting there and making my life miserable by converting my bank balance into a negative number.
The only benefit to an overdraft is lower 'repayment', if you want to look at it like that, because the only direct cost is the interest you owe that is added directly to the overdraft ... unlike a credit card, which has the interest PLUS a minimum repayment factored in. I'd say that my credit card repayments have always been at least three times higher than my overdraft payment, so that's maybe something to consider?
Go for a credit card if you want to feel guilty about your debt and have an enforced payment structure to clear it.
Go for an overdraft if you need access to credit and you don't think you're going to have money in the short-term to pay it back, so you'd rather just let it build up interest or cover at least that much (bear in mind you don't want to go into overdraft on your overdraft so never use more than you can afford lol).
In terms of interest rates, I think both of mine are very close to each other (within 2% difference), so that's not a factor, but I've probably ended up paying stacks more interest on my overdraft simply because that's all I pay ... while I rather divert my money to paying off the credit cards/other 'visible' debt.