Can't say it was a bad experience for me with the debit card. I've been charged ~10 times for the same plane ticket once (most likely charged until the bank refused more overdraft). Got a message about an overdraft straight-away on my mobile, called the bank, said only "that's a mistake, there should be only one" and the transactions were reverted immediately. (then the airline refunded them on their end again and reverted the refund when they realised the bank was faster, but in the end the balance was ok)
So yeah, in theory it's easier to get the credit card charge disputed. In practice, it probably depends on your bank a lot. This happened in the UK btw.
The balance was not ok when I reported it. The bank reverted the transactions immediately, without contacting the merchant. It was while I was still ~2k below.
Which bank are you with? I'm on Lloyd's Bank (what used to be Lloyd's TSB), and they won't send me a text message or email when I go into overdraft, only snail mail.
So yeah, in theory it's easier to get the credit card charge disputed. In practice, it probably depends on your bank a lot. This happened in the UK btw.