Part of the inconsistency in the UK is unique to the UK. There is additional protection under Section 75 for credit card purchases (over £100). So chargeback on debit cards and credit cards is different.
Section 75 doesn't apply in Ireland, so you're relying on the card scheme rules, and your bank to process a chargeback.
The chargeback rules are set by the scheme (Visa/MasterCard, etc). Part of the rules are that you have to have tried to resolve the issue first directly with the merchant. The banks ask that you declare you've tried to resolve the matter directly. The bit that I'm not clear on is if the merchant offers you a credit note / voucher, is that it 'resolved' from the chargeback point of view? AIB for example have updated their chargeback claim form to say that if you've been offered a voucher / credit by merchant, then they cannot currently accept a chargeback claim.
It must be remembered that with scheme chargeback the merchant can dispute a chargeback, and when they do, there is automatically a fee charged to your bank. This is about 40 euro per transaction, so they'd add up with high volumes, and in practice Banks very very rarely pass this charge on to the customer. It's one of the reasons that banks are becoming selective in processing chargebacks, and looking for more evidence to support them now. You must have exhausted your options with the merchant before using chargeback.