Make sure that all of the Delta miles get transferred into your Delta account (they should be once your statement closes). Then, you can cancel the card without losing any miles. They will remain in your Delta account, not AMEX. When does your annual fee come due? I would wait until it is almost due or has just hit and then call to cancel. They may even offer to waive the fee.
I have the Sapphire Preferred and Freedom. With Chase, you can use points to pay for travel directly, get cash back, or transfer to their partners. Partners include United, Hyatt, Southwest, Virgin Atlantic. With the Sapphire you get 2X points dining and travel, it has no foreign transaction fees, and now it has the chip technology. The Freedom has 5X categories every quarter (groceries, gas, amazon, etc.) and, if you have the sapphire as well, you can transfer points to partners. I think the sapphire bonus is 40k points and freedom is 10k points, so you'd end up with at least $500 worth of free travel.