The Credit Card Offer

For several years, a credit card holder had been using a cash-back rewards credit card issued by a major credit card company. He received an email from his mobile phone provider, letting him know that the company was introducing a new rewards card with lower rewards but also a lower annual fee than his current card. The credit card user suspected there might be a level of spending at which one card was preferable to the other, but he thought it might be difficult to find that level because of the structure of the reward tiers offered by his existing card. He also wondered whether the new card would have the same convenience and protections as his old one. How could he evaluate these other factors?