Banking can sometimes be a lot like baking. Change an ingredient and you change the result.
Sometime ago I changed my bank account to reflect my usage. I changed from a monthly fee to a free, pay per debit charge plan. The side-effect was that the fee on my credit card was no longer waived. The annual fee was less than the total monthly fees on the bank account, but it was still annoying.
I didn’t want to close my credit card account, however, because it had a 12 year history, and removing that would affect my credit score, which is something I want to keep relatively intact.
What I then thought about, and confirmed through a phone call, is that changing cards on the same account keeps the account in tact, so does not affect your score. Doing so keeps the same account active, and the information still flowing to the reporting agencies.
To clarify, your credit card is merely the piece of plastic. Your credit account is broader, and dates back to when you first applied for credit with a particular provider. In my case, I have had 3 credit cards on the same account. The first was a student card, the second was the normal version of the previous card that I switched to after graduation, and now a third card. However, my account is the same 12-year-old account.
You may not be able to switch from, say, a point card to an airmiles card, or a gas point card to a cash-back card (check with your provider), but you should be able to switch to a similarly structured card with the same provider. I switched to a no annual fee card that has the same point system (though it accumulates at a slower rate), so I can still use my points toward my RRSP or TFSA. I also ended up getting half of my last fee credited back to my account. The change also gives me some better travel insurance, and extended warranty of products bought with the card.
When it comes down to it, unless you are putting a lot of purchases on your card to justify the annual fee, you are probably better off with a no-fee card. Calling to change cards on the same account will save you money and leave your credit score untouched.